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%!
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% PostScript prologue for pstricks.tex.
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% Version 97 patch 4, 04/05/10
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% For distribution, see pstricks.tex.
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%
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/tx@Dict 200 dict def tx@Dict begin
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/ADict 25 dict def
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/CM { matrix currentmatrix } bind def
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/CP /currentpoint load def
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/ED { exch def } bind def
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/L /lineto load def
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/T /translate load def
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/TMatrix { } def
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/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }
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def
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/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
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} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
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/pathforall load stopped { pop pop pop pop } if z } def
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%
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%%-------------- DG begin patch 15 ---------------%%
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%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
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%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
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%0 } ifelse setdash stroke } def
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/DashLine {
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dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
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/b ED /x1 ED /y1 ED /x ED /y ED
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/z y x add y1 add x1 add def
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/Coef b a .5 sub 2 mul y mul sub z Div round
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z mul a .5 sub 2 mul y mul add b exch Div def
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/y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def
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x1 0 gt y1 0 gt x 0 gt y 0 gt and { [ y x y1 x1 ] 1 a sub y mul}
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{ [ 1 0] 0 } ifelse setdash stroke
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} def
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%%-------------- DG end patch 15 ---------------%%
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{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add
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def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if
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] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1
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setlinecap stroke } def
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/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
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2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
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% DG/SR modification begin - Dec. 12, 1997 - Patch 2
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%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
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itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
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% DG/SR modification end
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Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
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/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
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% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
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% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
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% def
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a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
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pop pop } def
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% DG/SR modification end
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/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
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exch 3 index sub exch Atan rotate newpath } def
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/EndArrow { @mtrx setmatrix CP grestore end } def
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/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1
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scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
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grestore } def
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/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
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CLW moveto } def
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/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
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div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
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CLW moveto } def
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/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
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2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
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curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }
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def
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/SD { 0 360 arc fill } def
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/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS
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/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
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load } if ] cvx newpath 3 1 roll T exec } def
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/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
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cvi def } def
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/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
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f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
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/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub
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def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def
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/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
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ifelse { pop } repeat a } def
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/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
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and { pop pop /n n 1 sub def } if } def
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/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
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repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
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ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
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moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
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Lineto pop pop closepath } ifelse } def
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/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
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neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
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def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
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div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
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setmatrix } def
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% DG modification begin - Jan. 15, 1997
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%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
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%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
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%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
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%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
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%setmatrix } def
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/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
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CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
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div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
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d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
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% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
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% setmatrix } def
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setmatrix pop } def
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% DG/SR modification end
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/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
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def } def
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/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
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def } def
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/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
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def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
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mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
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abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
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/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
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m mul neg def } def
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/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
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ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
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def
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/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
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/NC { CC x1 y1 x2 y2 x y curveto } def
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/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
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/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
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/NAC { x2 y2 x y curveto CC x1 y1 } def
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/EAC { x2 y2 x y ArrowB curveto pop pop } def
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/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def
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n { NC } repeat EOC } ifelse } def
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/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
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/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
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pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
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/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
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CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
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repeat closepath pop pop } ifelse } def
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/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
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/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
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/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
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def
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/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
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rotate matrix concatmatrix exch findfont exch makefont setfont } def
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/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
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x1 y1 lineto closepath } def
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/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
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y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
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exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
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/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
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x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
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ifelse } def
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/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
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/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
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pop pop Rect } { OvalFrame } ifelse } def
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225 |
/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
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} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
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aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
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/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
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2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
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ifelse } def
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/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
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6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
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/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
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sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
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def
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/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
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sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
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x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
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y0 x0 2 mul x1 sub y1 ] def } def
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/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }
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if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if
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/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div
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round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
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round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
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0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def
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/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }
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if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }
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{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
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exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
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div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
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dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {
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dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {
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pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup
|
|
254 |
stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}
|
|
255 |
{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i
|
|
256 |
w add def } repeat grestore gsave n 0 gt
|
|
257 |
% DG/SR modification begin - Nov. 7, 1997 - Patch 1
|
|
258 |
%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
|
|
259 |
{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
|
|
260 |
% DG/SR modification end
|
|
261 |
{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul
|
|
262 |
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
|
|
263 |
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
|
|
264 |
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
|
|
265 |
dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt
|
|
266 |
{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g
|
|
267 |
exch t L stroke /i i h add def } repeat grestore } def
|
|
268 |
/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0
|
|
269 |
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
|
|
270 |
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
|
|
271 |
mul neg d } def
|
|
272 |
/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
|
|
273 |
/Rot { CP CP translate 3 -1 roll neg rotate NET } def
|
|
274 |
/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }
|
|
275 |
def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle
|
|
276 |
dup a add ] cvx def } def
|
|
277 |
/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
|
|
278 |
cvx def } def
|
|
279 |
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
|
|
280 |
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
|
|
281 |
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
|
|
282 |
/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
|
|
283 |
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
|
|
284 |
div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
|
|
285 |
h1 abs h sub dup s mul abs } ifelse } def
|
|
286 |
/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
|
|
287 |
mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
|
|
288 |
{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
|
|
289 |
exch } def
|
|
290 |
/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
|
|
291 |
/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
|
|
292 |
} if } ifelse } def
|
|
293 |
/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
|
|
294 |
/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
|
|
295 |
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
|
|
296 |
/IfVisible true def } def
|
|
297 |
end
|
|
298 |
% END pstricks.pro
|
|
299 |
|
|
300 |
%%EndProcSet
|
|
301 |
%%BeginProcSet: pst-dots.pro 0 0
|
|
302 |
%!PS-Adobe-2.0
|
|
303 |
%%Title: Dot Font for PSTricks
|
|
304 |
%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>
|
|
305 |
%%Creation Date: May 7, 1993
|
|
306 |
%% Version 97 patch 1, 99/12/16
|
|
307 |
%% Modified by Etienne Riga <etienne.riga@skynet.be> - Dec. 16, 1999
|
|
308 |
%% to add /Diamond, /SolidDiamond and /BoldDiamond
|
|
309 |
10 dict dup begin
|
|
310 |
/FontType 3 def
|
|
311 |
/FontMatrix [ .001 0 0 .001 0 0 ] def
|
|
312 |
/FontBBox [ 0 0 0 0 ] def
|
|
313 |
/Encoding 256 array def
|
|
314 |
0 1 255 { Encoding exch /.notdef put } for
|
|
315 |
Encoding
|
|
316 |
dup (b) 0 get /Bullet put
|
|
317 |
dup (c) 0 get /Circle put
|
|
318 |
dup (C) 0 get /BoldCircle put
|
|
319 |
dup (u) 0 get /SolidTriangle put
|
|
320 |
dup (t) 0 get /Triangle put
|
|
321 |
dup (T) 0 get /BoldTriangle put
|
|
322 |
dup (r) 0 get /SolidSquare put
|
|
323 |
dup (s) 0 get /Square put
|
|
324 |
dup (S) 0 get /BoldSquare put
|
|
325 |
dup (q) 0 get /SolidPentagon put
|
|
326 |
dup (p) 0 get /Pentagon put
|
|
327 |
dup (P) 0 get /BoldPentagon put
|
|
328 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
329 |
dup (l) 0 get /SolidDiamond put
|
|
330 |
dup (d) 0 get /Diamond put
|
|
331 |
(D) 0 get /BoldDiamond put
|
|
332 |
% DG/SR modification end
|
|
333 |
/Metrics 13 dict def
|
|
334 |
Metrics begin
|
|
335 |
/Bullet 1000 def
|
|
336 |
/Circle 1000 def
|
|
337 |
/BoldCircle 1000 def
|
|
338 |
/SolidTriangle 1344 def
|
|
339 |
/Triangle 1344 def
|
|
340 |
/BoldTriangle 1344 def
|
|
341 |
/SolidSquare 886 def
|
|
342 |
/Square 886 def
|
|
343 |
/BoldSquare 886 def
|
|
344 |
/SolidPentagon 1093.2 def
|
|
345 |
/Pentagon 1093.2 def
|
|
346 |
/BoldPentagon 1093.2 def
|
|
347 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
348 |
/SolidDiamond 1008 def
|
|
349 |
/Diamond 1008 def
|
|
350 |
/BoldDiamond 1008 def
|
|
351 |
% DG/SR modification end
|
|
352 |
/.notdef 0 def
|
|
353 |
end
|
|
354 |
/BBoxes 13 dict def
|
|
355 |
BBoxes begin
|
|
356 |
/Circle { -550 -550 550 550 } def
|
|
357 |
/BoldCircle /Circle load def
|
|
358 |
/Bullet /Circle load def
|
|
359 |
/Triangle { -571.5 -330 571.5 660 } def
|
|
360 |
/BoldTriangle /Triangle load def
|
|
361 |
/SolidTriangle /Triangle load def
|
|
362 |
/Square { -450 -450 450 450 } def
|
|
363 |
/BoldSquare /Square load def
|
|
364 |
/SolidSquare /Square load def
|
|
365 |
/Pentagon { -546.6 -465 546.6 574.7 } def
|
|
366 |
/BoldPentagon /Pentagon load def
|
|
367 |
/SolidPentagon /Pentagon load def
|
|
368 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
369 |
/Diamond { -428.5 -742.5 428.5 742.5 } def
|
|
370 |
/BoldDiamond /Diamond load def
|
|
371 |
/SolidDiamond /Diamond load def
|
|
372 |
% DG/SR modification end
|
|
373 |
/.notdef { 0 0 0 0 } def
|
|
374 |
end
|
|
375 |
/CharProcs 20 dict def
|
|
376 |
CharProcs begin
|
|
377 |
/Adjust {
|
|
378 |
2 copy dtransform floor .5 add exch floor .5 add exch idtransform
|
|
379 |
3 -1 roll div 3 1 roll exch div exch scale
|
|
380 |
} def
|
|
381 |
/CirclePath { 0 0 500 0 360 arc closepath } def
|
|
382 |
/Bullet { 500 500 Adjust CirclePath fill } def
|
|
383 |
/Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath
|
|
384 |
eofill } def
|
|
385 |
/BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath
|
|
386 |
eofill } def
|
|
387 |
/BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def
|
|
388 |
/TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto
|
|
389 |
closepath } def
|
|
390 |
/SolidTriangle { TrianglePath fill } def
|
|
391 |
/Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def
|
|
392 |
/BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def
|
|
393 |
/SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto
|
|
394 |
-450 -450 lineto closepath } def
|
|
395 |
/SolidSquare { SquarePath fill } def
|
|
396 |
/Square { SquarePath .89 .89 scale SquarePath eofill } def
|
|
397 |
/BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def
|
|
398 |
/PentagonPath {
|
|
399 |
-337.8 -465 moveto
|
|
400 |
337.8 -465 lineto
|
|
401 |
546.6 177.6 lineto
|
|
402 |
0 574.7 lineto
|
|
403 |
-546.6 177.6 lineto
|
|
404 |
closepath
|
|
405 |
} def
|
|
406 |
/SolidPentagon { PentagonPath fill } def
|
|
407 |
/Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def
|
|
408 |
/BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def
|
|
409 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
410 |
/DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
|
|
411 |
428.5 0 lineto closepath } def
|
|
412 |
/SolidDiamond { DiamondPath fill } def
|
|
413 |
/Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def
|
|
414 |
/BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def
|
|
415 |
% DG/SR modification end
|
|
416 |
/.notdef { } def
|
|
417 |
end
|
|
418 |
/BuildGlyph {
|
|
419 |
exch
|
|
420 |
begin
|
|
421 |
Metrics 1 index get exec 0
|
|
422 |
BBoxes 3 index get exec
|
|
423 |
setcachedevice
|
|
424 |
CharProcs begin load exec end
|
|
425 |
end
|
|
426 |
} def
|
|
427 |
/BuildChar {
|
|
428 |
1 index /Encoding get exch get
|
|
429 |
1 index /BuildGlyph get exec
|
|
430 |
} bind def
|
|
431 |
end
|
|
432 |
/PSTricksDotFont exch definefont pop
|
|
433 |
%END pst-dots.pro
|
|
434 |
|
|
435 |
%%EndProcSet
|
|
436 |
%%BeginProcSet: pst-node.pro 0 0
|
|
437 |
%!
|
|
438 |
% PostScript prologue for pst-node.tex.
|
|
439 |
% Version 97 patch 1, 97/05/09.
|
|
440 |
% For distribution, see pstricks.tex.
|
|
441 |
%
|
|
442 |
/tx@NodeDict 400 dict def tx@NodeDict begin
|
|
443 |
tx@Dict begin /T /translate load def end
|
|
444 |
/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }
|
|
445 |
if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end
|
|
446 |
grestore } def
|
|
447 |
/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def
|
|
448 |
} def
|
|
449 |
/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch
|
|
450 |
Sin mul } def } def
|
|
451 |
/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def
|
|
452 |
} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }
|
|
453 |
ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx
|
|
454 |
dup Sin mul Cos Div } ifelse } def
|
|
455 |
/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub
|
|
456 |
/u ED /NodePos { GetRnodePos } def } def
|
|
457 |
/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
|
|
458 |
Cos mul exch Sin mul } def
|
|
459 |
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
|
|
460 |
mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul
|
|
461 |
} ifelse } def
|
|
462 |
/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d
|
|
463 |
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
|
|
464 |
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
|
|
465 |
sin def /NodePos { TriNodePos } def } def
|
|
466 |
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
|
|
467 |
hh mul Atan dup cos ww mul exch sin hh mul } def
|
|
468 |
/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
|
|
469 |
/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist
|
|
470 |
Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }
|
|
471 |
{ 0 Dist Sin mul } ifelse } ifelse Do } def
|
|
472 |
/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform
|
|
473 |
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
|
|
474 |
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
|
|
475 |
XYPos } ifelse } def
|
|
476 |
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
|
|
477 |
roll sin mul sub exch } ifelse } def
|
|
478 |
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
|
|
479 |
AddOffset yA add /yA1 ED xA add /xA1 ED } def
|
|
480 |
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
|
|
481 |
AddOffset yB add /yB1 ED xB add /xB1 ED } def
|
|
482 |
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
|
|
483 |
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
|
|
484 |
ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED
|
|
485 |
} ifelse } def
|
|
486 |
/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB
|
|
487 |
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
|
|
488 |
ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED
|
|
489 |
} ifelse } def
|
|
490 |
/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED
|
|
491 |
/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b
|
|
492 |
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
|
|
493 |
ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def
|
|
494 |
/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub
|
|
495 |
mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def
|
|
496 |
/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt
|
|
497 |
{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop
|
|
498 |
} repeat LPutLine cleartomark } def
|
|
499 |
/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED
|
|
500 |
/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3
|
|
501 |
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
|
|
502 |
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
|
|
503 |
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
|
|
504 |
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
|
|
505 |
mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def
|
|
506 |
/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
|
|
507 |
} def
|
|
508 |
/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
|
|
509 |
/NAngle yyB yyA sub xxB xxA sub Atan def } def
|
|
510 |
/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
|
|
511 |
/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
|
|
512 |
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
|
|
513 |
} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
|
|
514 |
} def
|
|
515 |
/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
|
|
516 |
} def
|
|
517 |
/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
|
|
518 |
/NAngle yyB yyA sub xxB xxA sub Atan def } def
|
|
519 |
/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
|
|
520 |
/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
|
|
521 |
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
|
|
522 |
exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
|
|
523 |
VPosEnd } def
|
|
524 |
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
|
|
525 |
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
|
|
526 |
def grestore exec /LPutVar /SaveLPutVar load def } def
|
|
527 |
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
|
|
528 |
GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {
|
|
529 |
LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {
|
|
530 |
LPutVar VPutLine } def LPutVar } def
|
|
531 |
/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop
|
|
532 |
end } def
|
|
533 |
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
|
|
534 |
Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan
|
|
535 |
/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1
|
|
536 |
yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {
|
|
537 |
LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
|
|
538 |
ifelse } def
|
|
539 |
/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
|
|
540 |
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
|
|
541 |
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
|
|
542 |
begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
|
|
543 |
cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
|
|
544 |
} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
|
|
545 |
/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
|
|
546 |
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
|
|
547 |
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
|
|
548 |
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
|
|
549 |
yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def
|
|
550 |
/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def
|
|
551 |
/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2
|
|
552 |
yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
|
|
553 |
/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1
|
|
554 |
tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]
|
|
555 |
cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
|
|
556 |
VPutLines } def } def
|
|
557 |
/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def
|
|
558 |
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
|
|
559 |
transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }
|
|
560 |
{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB
|
|
561 |
0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict
|
|
562 |
begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx
|
|
563 |
def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
|
|
564 |
VPutLines } def } def
|
|
565 |
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
|
|
566 |
xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end
|
|
567 |
/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
|
|
568 |
LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
|
|
569 |
def
|
|
570 |
/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
|
|
571 |
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
|
|
572 |
false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
|
|
573 |
LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
|
|
574 |
def
|
|
575 |
/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
|
|
576 |
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
|
|
577 |
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
|
|
578 |
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
|
|
579 |
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
|
|
580 |
Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
|
|
581 |
cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
|
|
582 |
VPutLines } def } def
|
|
583 |
% DG/SR modification begin - May 9, 1997 - Patch 1
|
|
584 |
%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
|
|
585 |
%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
|
|
586 |
%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
|
|
587 |
%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
|
|
588 |
/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r
|
|
589 |
r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
|
|
590 |
exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
|
|
591 |
mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
|
|
592 |
% DG/SR modification end
|
|
593 |
} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add
|
|
594 |
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
|
|
595 |
Div def /y ED /x ED } def
|
|
596 |
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
|
|
597 |
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
|
|
598 |
mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def
|
|
599 |
/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy
|
|
600 |
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
|
|
601 |
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
|
|
602 |
tx@Dict begin false Polygon end } def
|
|
603 |
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
|
|
604 |
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
|
|
605 |
mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
|
|
606 |
/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div
|
|
607 |
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
|
|
608 |
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
|
|
609 |
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
|
|
610 |
eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }
|
|
611 |
{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def
|
|
612 |
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
|
|
613 |
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
|
|
614 |
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
|
|
615 |
roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }
|
|
616 |
ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos
|
|
617 |
{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {
|
|
618 |
r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }
|
|
619 |
{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add
|
|
620 |
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
|
|
621 |
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
|
|
622 |
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
|
|
623 |
y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {
|
|
624 |
LPutPos } def } def
|
|
625 |
/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
|
|
626 |
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
|
|
627 |
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
|
|
628 |
w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
|
|
629 |
{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
|
|
630 |
{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
|
|
631 |
def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
|
|
632 |
/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
|
|
633 |
/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg
|
|
634 |
exch X sub neg exch moveto setmatrix CP grestore } def
|
|
635 |
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
|
|
636 |
def } ifelse LPutCoor } def
|
|
637 |
/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }
|
|
638 |
if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }
|
|
639 |
ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }
|
|
640 |
def
|
|
641 |
/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if
|
|
642 |
r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }
|
|
643 |
ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }
|
|
644 |
def
|
|
645 |
end
|
|
646 |
% END pst-node.pro
|
|
647 |
|
|
648 |
%%EndProcSet
|
|
649 |
%%BeginProcSet: 8r.enc 0 0
|
|
650 |
% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30
|
|
651 |
%
|
|
652 |
% @@psencodingfile@{
|
|
653 |
% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry,
|
|
654 |
% W. Schmidt, P. Lehman",
|
|
655 |
% version = "2.0",
|
|
656 |
% date = "30 October 2002",
|
|
657 |
% filename = "8r.enc",
|
|
658 |
% email = "tex-fonts@@tug.org",
|
|
659 |
% docstring = "This is the encoding vector for Type1 and TrueType
|
|
660 |
% fonts to be used with TeX. This file is part of the
|
|
661 |
% PSNFSS bundle, version 9"
|
|
662 |
% @}
|
|
663 |
%
|
|
664 |
% The idea is to have all the characters normally included in Type 1 fonts
|
|
665 |
% available for typesetting. This is effectively the characters in Adobe
|
|
666 |
% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol,
|
|
667 |
% MacRoman, and some extra characters from Lucida.
|
|
668 |
%
|
|
669 |
% Character code assignments were made as follows:
|
|
670 |
%
|
|
671 |
% (1) the Windows ANSI characters are almost all in their Windows ANSI
|
|
672 |
% positions, because some Windows users cannot easily reencode the
|
|
673 |
% fonts, and it makes no difference on other systems. The only Windows
|
|
674 |
% ANSI characters not available are those that make no sense for
|
|
675 |
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
|
|
676 |
% (173). quotesingle and grave are moved just because it's such an
|
|
677 |
% irritation not having them in TeX positions.
|
|
678 |
%
|
|
679 |
% (2) Remaining characters are assigned arbitrarily to the lower part
|
|
680 |
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
|
|
681 |
%
|
|
682 |
% (3) Y&Y Lucida Bright includes some extra text characters; in the
|
|
683 |
% hopes that other PostScript fonts, perhaps created for public
|
|
684 |
% consumption, will include them, they are included starting at 0x12.
|
|
685 |
% These are /dotlessj /ff /ffi /ffl.
|
|
686 |
%
|
|
687 |
% (4) hyphen appears twice for compatibility with both ASCII and Windows.
|
|
688 |
%
|
|
689 |
% (5) /Euro was assigned to 128, as in Windows ANSI
|
|
690 |
%
|
|
691 |
% (6) Missing characters from MacRoman encoding incorporated as follows:
|
|
692 |
%
|
|
693 |
% PostScript MacRoman TeXBase1
|
|
694 |
% -------------- -------------- --------------
|
|
695 |
% /notequal 173 0x16
|
|
696 |
% /infinity 176 0x17
|
|
697 |
% /lessequal 178 0x18
|
|
698 |
% /greaterequal 179 0x19
|
|
699 |
% /partialdiff 182 0x1A
|
|
700 |
% /summation 183 0x1B
|
|
701 |
% /product 184 0x1C
|
|
702 |
% /pi 185 0x1D
|
|
703 |
% /integral 186 0x81
|
|
704 |
% /Omega 189 0x8D
|
|
705 |
% /radical 195 0x8E
|
|
706 |
% /approxequal 197 0x8F
|
|
707 |
% /Delta 198 0x9D
|
|
708 |
% /lozenge 215 0x9E
|
|
709 |
%
|
|
710 |
/TeXBase1Encoding [
|
|
711 |
% 0x00
|
|
712 |
/.notdef /dotaccent /fi /fl
|
|
713 |
/fraction /hungarumlaut /Lslash /lslash
|
|
714 |
/ogonek /ring /.notdef /breve
|
|
715 |
/minus /.notdef /Zcaron /zcaron
|
|
716 |
% 0x10
|
|
717 |
/caron /dotlessi /dotlessj /ff
|
|
718 |
/ffi /ffl /notequal /infinity
|
|
719 |
/lessequal /greaterequal /partialdiff /summation
|
|
720 |
/product /pi /grave /quotesingle
|
|
721 |
% 0x20
|
|
722 |
/space /exclam /quotedbl /numbersign
|
|
723 |
/dollar /percent /ampersand /quoteright
|
|
724 |
/parenleft /parenright /asterisk /plus
|
|
725 |
/comma /hyphen /period /slash
|
|
726 |
% 0x30
|
|
727 |
/zero /one /two /three
|
|
728 |
/four /five /six /seven
|
|
729 |
/eight /nine /colon /semicolon
|
|
730 |
/less /equal /greater /question
|
|
731 |
% 0x40
|
|
732 |
/at /A /B /C
|
|
733 |
/D /E /F /G
|
|
734 |
/H /I /J /K
|
|
735 |
/L /M /N /O
|
|
736 |
% 0x50
|
|
737 |
/P /Q /R /S
|
|
738 |
/T /U /V /W
|
|
739 |
/X /Y /Z /bracketleft
|
|
740 |
/backslash /bracketright /asciicircum /underscore
|
|
741 |
% 0x60
|
|
742 |
/quoteleft /a /b /c
|
|
743 |
/d /e /f /g
|
|
744 |
/h /i /j /k
|
|
745 |
/l /m /n /o
|
|
746 |
% 0x70
|
|
747 |
/p /q /r /s
|
|
748 |
/t /u /v /w
|
|
749 |
/x /y /z /braceleft
|
|
750 |
/bar /braceright /asciitilde /.notdef
|
|
751 |
% 0x80
|
|
752 |
/Euro /integral /quotesinglbase /florin
|
|
753 |
/quotedblbase /ellipsis /dagger /daggerdbl
|
|
754 |
/circumflex /perthousand /Scaron /guilsinglleft
|
|
755 |
/OE /Omega /radical /approxequal
|
|
756 |
% 0x90
|
|
757 |
/.notdef /.notdef /.notdef /quotedblleft
|
|
758 |
/quotedblright /bullet /endash /emdash
|
|
759 |
/tilde /trademark /scaron /guilsinglright
|
|
760 |
/oe /Delta /lozenge /Ydieresis
|
|
761 |
% 0xA0
|
|
762 |
/.notdef /exclamdown /cent /sterling
|
|
763 |
/currency /yen /brokenbar /section
|
|
764 |
/dieresis /copyright /ordfeminine /guillemotleft
|
|
765 |
/logicalnot /hyphen /registered /macron
|
|
766 |
% 0xD0
|
|
767 |
/degree /plusminus /twosuperior /threesuperior
|
|
768 |
/acute /mu /paragraph /periodcentered
|
|
769 |
/cedilla /onesuperior /ordmasculine /guillemotright
|
|
770 |
/onequarter /onehalf /threequarters /questiondown
|
|
771 |
% 0xC0
|
|
772 |
/Agrave /Aacute /Acircumflex /Atilde
|
|
773 |
/Adieresis /Aring /AE /Ccedilla
|
|
774 |
/Egrave /Eacute /Ecircumflex /Edieresis
|
|
775 |
/Igrave /Iacute /Icircumflex /Idieresis
|
|
776 |
% 0xD0
|
|
777 |
/Eth /Ntilde /Ograve /Oacute
|
|
778 |
/Ocircumflex /Otilde /Odieresis /multiply
|
|
779 |
/Oslash /Ugrave /Uacute /Ucircumflex
|
|
780 |
/Udieresis /Yacute /Thorn /germandbls
|
|
781 |
% 0xE0
|
|
782 |
/agrave /aacute /acircumflex /atilde
|
|
783 |
/adieresis /aring /ae /ccedilla
|
|
784 |
/egrave /eacute /ecircumflex /edieresis
|
|
785 |
/igrave /iacute /icircumflex /idieresis
|
|
786 |
% 0xF0
|
|
787 |
/eth /ntilde /ograve /oacute
|
|
788 |
/ocircumflex /otilde /odieresis /divide
|
|
789 |
/oslash /ugrave /uacute /ucircumflex
|
|
790 |
/udieresis /yacute /thorn /ydieresis
|
|
791 |
] def
|
|
792 |
|
|
793 |
|
|
794 |
%%EndProcSet
|
|
795 |
%%BeginProcSet: texps.pro 0 0
|
|
796 |
%!
|
|
797 |
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
|
|
798 |
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
|
|
799 |
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
|
|
800 |
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
|
|
801 |
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
|
|
802 |
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
|
|
803 |
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
|
|
804 |
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
|
|
805 |
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
|
|
806 |
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
|
|
807 |
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
|
|
808 |
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
|
|
809 |
end
|
|
810 |
|
|
811 |
%%EndProcSet
|
|
812 |
%%BeginProcSet: special.pro 0 0
|
|
813 |
%!
|
|
814 |
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
|
|
815 |
/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
|
|
816 |
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
|
|
817 |
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
|
|
818 |
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
|
|
819 |
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
|
|
820 |
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
|
|
821 |
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
|
|
822 |
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
|
|
823 |
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
|
|
824 |
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
|
|
825 |
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
|
|
826 |
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
|
|
827 |
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
|
|
828 |
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
|
|
829 |
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
|
|
830 |
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2804 |
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2805 |
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3940 |
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3945 |
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3947 |
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3948 |
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3953 |
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3960 |
2076 2001 59 4 v 17 w Fq(f)10 b Fm(\))27 b Fq(;)83 2299
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3961 |
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3962 |
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(proofs.)f(Write)i Fm(\()p Fn(\000)p Fm(\))1750 2504
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(all)g(the)g(structure)h(on)f(a)h Fn(\003)p Fr(-polycate)o(gory)e
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3984 |
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3985 |
Fn(\003)p Fr(-polycate)o(gorical)e(formulation)h(structure)g(on)h(its)f
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4010 |
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4011 |
n(v)o(e)h(its)f(dual.)83 545 y Fo(3.1)100 b(Cate)l(gorical)23
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4012 |
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4013 |
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4014 |
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4015 |
(of)h Fn(C)1070 984 y Fw(id)1166 969 y Fr(of)g(idempotents,)e(which)h
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4016 |
(we)i(shall)e(call)h Fo(linear)f(idempotents)p Fr(.)f(In)83
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4017 |
1089 y(our)24 b(application)f(these)h(will)f(be)h(idempotents)e(\(maps)
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4018 |
h Fq(e)h Fr(with)f Fq(e)p Fm(;)17 b Fq(e)28 b Fm(=)g
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4019 |
Fq(e)p Fr(\))c(which)g(are)g(linear)g(in)g(the)83 1210
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4020 |
y(sense)31 b(of)g(2.2.2.)f(F)o(or)g(the)h(moment)e(we)i(need)g(assume)f
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4021 |
(nothing)f(be)o(yond)h(the)g(ob)o(vious)f(require-)83
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4022 |
1330 y(ment)c(that)f(e)n(v)o(ery)g(identity)f(is)i(in)f(the)h(class.)f
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4023 |
(W)-8 b(e)26 b(call)e(such)h(data)g(a)g Fo(guar)l(ded)f(cate)l(gory)p
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4024 |
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4025 |
(3.2.)p 0 TeXcolorgray 42 w Fo(A)f(guar)l(ded)f(functor)g
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4026 |
Fq(F)45 b Fm(:)32 b Fn(C)37 b(!)31 b(D)f Fr(between)d(guarded)g(cate)o
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4027 |
(gories)f(consists)f(of)83 1634 y(the)g(usual)g(data)g(for)h(a)g
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4028 |
(functor)f(such)g(that)f Fq(F)39 b Fr(maps)25 b(linear)g(idempotents)f
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4029 |
(to)g(linear)i(idempotents;)83 1755 y(and)f(whene)n(v)o(er)f
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4030 |
Fq(e)h Fr(and)g Fq(e)944 1718 y Fl(0)993 1755 y Fr(are)g(linear)g
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4031 |
(idempotents,)e(then)856 1992 y Fq(F)14 b Fm(\()p Fq(e)p
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4032 |
Fm(\);)j Fq(F)d Fm(\()p Fq(f)d Fm(\);)17 b Fq(F)d Fm(\()p
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4033 |
Fq(g)t Fm(\);)j Fq(F)d Fm(\()p Fq(e)1762 1950 y Fl(0)1783
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4034 |
1992 y Fm(\))27 b(=)h Fq(F)14 b Fm(\()p Fq(e)p Fm(\);)j
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4035 |
Fq(F)d Fm(\()p Fq(f)d Fm(;)17 b Fq(g)t Fm(\);)g Fq(F)d
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4036 |
Fm(\()p Fq(e)2705 1950 y Fl(0)2725 1992 y Fm(\))83 2229
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4037 |
y Fr(W)-8 b(e)27 b(say)g(that)f(a)h(guarded)f(functor)g
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4038 |
Fq(F)41 b Fr(is)26 b Fo(domain)f(absorbing)g Fr(when)h
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4039 |
Fq(F)14 b Fm(\()p Fq(e)p Fm(\);)j Fq(F)d Fm(\()p Fq(f)d
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4040 |
Fm(\))30 b(=)g Fq(F)14 b Fm(\()p Fq(e)p Fm(;)j Fq(f)11
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4041 |
b Fm(\))26 b Fr(for)83 2349 y(linear)j(idempotents)e
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4042 |
Fq(e)p Fr(;)i(it)f(is)h Fo(codomain)f(absorbing)f Fr(when)h
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4043 |
Fq(F)14 b Fm(\()p Fq(f)d Fm(\);)17 b Fq(F)d Fm(\()p Fq(e)p
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Fk(A)1994 3619 y Fm(;)17 b Fq(G)p Fm(\()p Fq(u)p Fm(\);)g
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4081 |
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4101 |
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4104 |
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4106 |
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4107 |
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4108 |
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4110 |
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4111 |
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4112 |
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4113 |
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4114 |
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4116 |
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4121 |
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4122 |
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4123 |
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4128 |
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4129 |
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4130 |
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4135 |
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4146 |
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4147 |
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4149 |
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4150 |
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4151 |
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4152 |
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4157 |
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4159 |
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4160 |
Fq(e)495 3961 y Fk(B)581 3946 y Fo(and)i Fq(e)800 3961
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4161 |
y Fk(A)880 3946 y Fn(_)e Fq(e)1013 3961 y Fk(B)1074 3946
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4162 |
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4163 |
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4164 |
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4165 |
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4167 |
4364 y(that)30 b(means)f(in)g(case)i(of)f Fn(>)g Fr(and)g
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4168 |
Fn(?)p Fr(.\))g(W)-8 b(e)30 b(introduce)f(some)h(notation)e(for)i(the)g
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4169 |
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4170 |
(e)g(identi\002ed.)f(W)-8 b(e)25 b(write)510 4708 y Fq(e)555
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4171 |
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4194 |
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4196 |
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4206 |
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4210 |
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4212 |
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4631 |
|
|
4632 |
@endspecial Fn(_)949 388 y
|
|
4633 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4634 |
} false /N@B 16 {InitRnode } NewNode end end
|
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4635 |
949 388 a 20 w @beginspecial
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@setspecial
|
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tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
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0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
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grestore end
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4641 |
|
|
4642 |
@endspecial Fn(^)502 429 y
|
|
4643 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4644 |
} false /N@C 16 {InitRnode } NewNode end end
|
|
4645 |
502 429 a 20
|
|
4646 |
w @beginspecial @setspecial
|
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tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
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0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
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4650 |
grestore end
|
|
4651 |
|
|
4652 |
@endspecial Fn(^)1098 512
|
|
4653 |
y
|
|
4654 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4655 |
} false /N@D 16 {InitRnode } NewNode end end
|
|
4656 |
1098 512 a 20 w @beginspecial @setspecial
|
|
4657 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
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4658 |
0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add
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0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
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4660 |
grestore end
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4661 |
|
|
4662 |
@endspecial
|
|
4663 |
Fn(_)771 691 y
|
|
4664 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
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|
4665 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
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0.0 0 0 /N@A /N@AL InitNC { /AngleA -10. def /AngleB 180. def 0.67
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0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
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4668 |
grestore grestore end
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4669 |
771 691 a 771 691 a
|
|
4670 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4671 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
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|
4672 |
0.0 0 0 /N@A /N@BL InitNC { /AngleA 10. def /AngleB 180. def 0.67
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|
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0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4674 |
grestore grestore end
|
|
4675 |
771 691 a 771 691
|
|
4676 |
a
|
|
4677 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4678 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4679 |
0.0 0 0 /N@B /N@CR InitNC { /AngleA 170. def /AngleB 0. def 0.67
|
|
4680 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
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4681 |
grestore grestore end
|
|
4682 |
771 691 a 771 691 a
|
|
4683 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4684 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4685 |
0.0 0 0 /N@B /N@BR InitNC { /AngleA 190. def /AngleB 0. def 0.67
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|
4686 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
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|
4687 |
grestore grestore end
|
|
4688 |
771 691 a 771 691 a
|
|
4689 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4690 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4691 |
0.0 0 0 /N@C /N@CLL InitNC { /AngleA 10. def /AngleB 180. def 0.67
|
|
4692 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4693 |
grestore grestore end
|
|
4694 |
771 691 a 771
|
|
4695 |
691 a
|
|
4696 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4697 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4698 |
0.0 0 0 /N@C /N@A InitNC { /AngleA -10. def /AngleB 180. def 0.67
|
|
4699 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4700 |
grestore grestore end
|
|
4701 |
771 691 a 771 691 a
|
|
4702 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4703 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4704 |
0.0 0 0 /N@CL /N@CLL InitNC { NCLine } if end gsave 0.8 SLW 0 setgray
|
|
4705 |
0 setlinecap stroke grestore grestore end
|
|
4706 |
771 691 a 771 691 a
|
|
4707 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4708 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4709 |
0.0 0 0 /N@D /N@B InitNC { /AngleA 170. def /AngleB 0. def 0.67
|
|
4710 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4711 |
grestore grestore end
|
|
4712 |
771 691
|
|
4713 |
a 771 691 a
|
|
4714 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4715 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4716 |
0.0 0 0 /N@D /N@ARR InitNC { /AngleA 190. def /AngleB 0. def 0.67
|
|
4717 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4718 |
grestore grestore end
|
|
4719 |
771 691 a 771 691 a
|
|
4720 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4721 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4722 |
0.0 0 0 /N@AR /N@ARR InitNC { NCLine } if end gsave 0.8 SLW 0 setgray
|
|
4723 |
0 setlinecap stroke grestore grestore end
|
|
4724 |
771 691 a 1515 484 a
|
|
4725 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@E
|
|
4726 |
16 {InitRnode } NewNode end end
|
|
4727 |
|
|
4728 |
1515 484 a 192 402 a
|
|
4729 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@F
|
|
4730 |
16 {InitRnode } NewNode end end
|
|
4731 |
192 402 a 771 691 a
|
|
4732 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4733 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4734 |
0.0 0 0 /N@D /N@E InitNC { NCLine } if end gsave 0.8 SLW 0 setgray
|
|
4735 |
0 setlinecap stroke grestore grestore end
|
|
4736 |
771 691 a 771
|
|
4737 |
691 a
|
|
4738 |
tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end
|
|
4739 |
771 691 a 771 691 a
|
|
4740 |
tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 51.22697
|
|
4741 |
8.2125 2.73749 NAngle 90 add Uput exch pop add a PtoC h1 add exch
|
|
4742 |
w1 add exch } PutCoor PutBegin end
|
|
4743 |
771 691 a 558 714 a Fi(\()p
|
|
4744 |
Fj(A)5 b Fh(^)g Fj(B)g Fi(\))g Fh(_)g Fj(C)771 691 y
|
|
4745 |
tx@Dict begin PutEnd end
|
|
4746 |
|
|
4747 |
771 691 a 771 691 a
|
|
4748 |
tx@Dict begin PutEnd end
|
|
4749 |
771 691 a 771 691 a
|
|
4750 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4751 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4752 |
0.0 0 0 /N@C /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray
|
|
4753 |
0 setlinecap stroke grestore grestore end
|
|
4754 |
771 691 a 771
|
|
4755 |
691 a
|
|
4756 |
tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end
|
|
4757 |
771 691 a 771 691 a
|
|
4758 |
tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 51.22697
|
|
4759 |
8.2125 2.73749 NAngle 90 sub Uput exch pop add a PtoC h1 add exch
|
|
4760 |
w1 add exch } PutCoor PutBegin end
|
|
4761 |
771 691 a 558 714 a Fj(A)g
|
|
4762 |
Fh(^)g Fi(\()p Fj(B)10 b Fh(_)5 b Fj(C)i Fi(\))771 691
|
|
4763 |
y
|
|
4764 |
tx@Dict begin PutEnd end
|
|
4765 |
771 691 a 771 691 a
|
|
4766 |
tx@Dict begin PutEnd end
|
|
4767 |
771 691 a 1488 w @beginspecial
|
|
4768 |
@setspecial
|
|
4769 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833
|
|
4770 |
1.99179 15.93352 17.92503 .5 Frame gsave 0.85358 SLW 0 setgray 0
|
|
4771 |
setlinecap stroke grestore end
|
|
4772 |
|
|
4773 |
@endspecial 2297 628 a Fd(id)2338 639 y
|
|
4774 |
Fc(C)2259 691 y @beginspecial @setspecial
|
|
4775 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833
|
|
4776 |
21.90863 15.93352 37.84187 .5 Frame gsave 0.85358 SLW 0 setgray 0
|
|
4777 |
setlinecap stroke grestore end
|
|
4778 |
|
|
4779 |
@endspecial
|
|
4780 |
2296 463 a Fd(id)2337 474 y Fc(B)2259 691 y @beginspecial
|
|
4781 |
@setspecial
|
|
4782 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833
|
|
4783 |
41.82547 15.93352 57.75871 .5 Frame gsave 0.85358 SLW 0 setgray 0
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|
4784 |
setlinecap stroke grestore end
|
|
4785 |
|
|
4786 |
@endspecial 2297 298 a Fd(id)2338 309 y
|
|
4787 |
Fc(A)2292 278 y
|
|
4788 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@AL
|
|
4789 |
16 {InitRnode } NewNode end end
|
|
4790 |
2292 278 a 2292 443 a
|
|
4791 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@BL
|
|
4792 |
16 {InitRnode } NewNode end end
|
|
4793 |
2292 443 a 2292
|
|
4794 |
608 a
|
|
4795 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CL
|
|
4796 |
16 {InitRnode } NewNode end end
|
|
4797 |
2292 608 a 2159 608 a
|
|
4798 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CLL
|
|
4799 |
16 {InitRnode } NewNode end end
|
|
4800 |
2159 608 a 2391 278 a
|
|
4801 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@AR
|
|
4802 |
16 {InitRnode } NewNode end end
|
|
4803 |
2391
|
|
4804 |
278 a 2523 278 a
|
|
4805 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@ARR
|
|
4806 |
16 {InitRnode } NewNode end end
|
|
4807 |
2523 278 a 2391 443 a
|
|
4808 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@BR
|
|
4809 |
16 {InitRnode } NewNode end end
|
|
4810 |
2391 443 a 2391
|
|
4811 |
608 a
|
|
4812 |
tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CR
|
|
4813 |
16 {InitRnode } NewNode end end
|
|
4814 |
2391 608 a 2139 388 a
|
|
4815 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4816 |
} false /N@A 16 {InitRnode } NewNode end end
|
|
4817 |
2139 388 a 20 w @beginspecial
|
|
4818 |
@setspecial
|
|
4819 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
|
|
4820 |
0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add
|
|
4821 |
0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
|
|
4822 |
grestore end
|
|
4823 |
|
|
4824 |
@endspecial Fn(_)2437 553 y
|
|
4825 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4826 |
} false /N@B 16 {InitRnode } NewNode end end
|
|
4827 |
2437 553 a 20
|
|
4828 |
w @beginspecial @setspecial
|
|
4829 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
|
|
4830 |
0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add
|
|
4831 |
0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
|
|
4832 |
grestore end
|
|
4833 |
|
|
4834 |
@endspecial Fn(^)1991 512
|
|
4835 |
y
|
|
4836 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4837 |
} false /N@C 16 {InitRnode } NewNode end end
|
|
4838 |
1991 512 a 20 w @beginspecial @setspecial
|
|
4839 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
|
|
4840 |
0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add
|
|
4841 |
0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
|
|
4842 |
grestore end
|
|
4843 |
|
|
4844 |
@endspecial
|
|
4845 |
Fn(^)2586 429 y
|
|
4846 |
tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334
|
|
4847 |
} false /N@D 16 {InitRnode } NewNode end end
|
|
4848 |
2586 429 a 20 w @beginspecial @setspecial
|
|
4849 |
tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669
|
|
4850 |
0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add
|
|
4851 |
0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke
|
|
4852 |
grestore end
|
|
4853 |
|
|
4854 |
|
|
4855 |
@endspecial Fn(_)2259 691 y
|
|
4856 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4857 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4858 |
0.0 0 0 /N@A /N@AL InitNC { /AngleA 10. def /AngleB 180. def 0.67
|
|
4859 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4860 |
grestore grestore end
|
|
4861 |
2259 691 a 2259 691 a
|
|
4862 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4863 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4864 |
0.0 0 0 /N@A /N@BL InitNC { /AngleA -10. def /AngleB 180. def 0.67
|
|
4865 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4866 |
grestore grestore end
|
|
4867 |
2259
|
|
4868 |
691 a 2259 691 a
|
|
4869 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4870 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4871 |
0.0 0 0 /N@B /N@CR InitNC { /AngleA 190. def /AngleB 0. def 0.67
|
|
4872 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4873 |
grestore grestore end
|
|
4874 |
2259 691 a 2259 691 a
|
|
4875 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4876 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4877 |
0.0 0 0 /N@B /N@BR InitNC { /AngleA 170. def /AngleB 0. def 0.67
|
|
4878 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4879 |
grestore grestore end
|
|
4880 |
2259 691 a 2259
|
|
4881 |
691 a
|
|
4882 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4883 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4884 |
0.0 0 0 /N@C /N@CLL InitNC { /AngleA -10. def /AngleB 180. def 0.67
|
|
4885 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4886 |
grestore grestore end
|
|
4887 |
2259 691 a 2259 691 a
|
|
4888 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4889 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4890 |
0.0 0 0 /N@C /N@A InitNC { /AngleA 10. def /AngleB 180. def 0.67
|
|
4891 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4892 |
grestore grestore end
|
|
4893 |
2259 691 a 2259 691 a
|
|
4894 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4895 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4896 |
0.0 0 0 /N@CL /N@CLL InitNC { NCLine } if end gsave 0.8 SLW 0 setgray
|
|
4897 |
0 setlinecap stroke grestore grestore end
|
|
4898 |
2259
|
|
4899 |
691 a 2259 691 a
|
|
4900 |
tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto
|
|
4901 |
} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0
|
|
4902 |
0.0 0 0 /N@D /N@B InitNC { /AngleA 190. def /AngleB 0. def 0.67
|
|
4903 |
0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke
|
|
4904 |
grestore grestore end
|
|
4905 |
2259 691 a 2259 691 a
|
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5237 |
y Fk(A)712 1326 y Fn(\001)21 b Fm(id)843 1341 y Fk(B)931
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5243 |
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5258 |
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5259 |
Fm(\()p Fq(A)22 b Fn(^)h Fq(B)5 b Fm(;)17 b Fq(C)29 b
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5260 |
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5274 |
Fw(\000)1393 2676 y Fm(;)17 b Fq(f)11 b Fm(;)17 b Fq(e)1585
|
|
5275 |
2642 y Ff(W)1666 2700 y Fw(\001)1772 2676 y Fm(=)43 b
|
|
5276 |
Fq(f)11 b Fr(.)33 b(Finally)g(we)g(ha)n(v)o(e)g(a)h(series)f(of)g
|
|
5277 |
(\002ddly)g(b)n(ut)83 2796 y(routine)25 b(tasks.)p 0
|
|
5278 |
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|
5279 |
b(e)34 b(sho)n(w)d(that)i Fn(C)6 b Fm(\(\000;)17 b(\001\))33
|
|
5280 |
b Fr(is)f(essentially)g(independent)g(of)h(the)f(brack)o(eting)h
|
|
5281 |
(chosen.)f(This)289 3094 y(follo)n(ws)24 b(from)g(the)h(coherence)h(of)
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|
5282 |
e(the)h(canonical)g(linear)f(idempotents.)p 0 TeXcolorgray
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|
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|
5285 |
h(combines)g(point)289 3334 y(\(1\))36 b(with)f(hea)n(vy)h(use)g(of)g
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|
5286 |
(the)g(linear)f(distrib)n(uti)n(vities.)d(And)k(we)g(sho)n(w)f(that)g
|
|
5287 |
(the)h(result)f(is)289 3455 y(indeed)25 b(a)g Fn(\003)p
|
|
5288 |
Fr(-polycate)o(gory)-6 b(.)p 0 TeXcolorgray 123 3575
|
|
5289 |
a(\(3\))p 0 TeXcolorgray 50 w(W)e(e)37 b(de\002ne)f(the)g(logical)f
|
|
5290 |
(operations)g(on)g(the)h(collections)f(of)h(polymaps)e(and)i(deri)n(v)o
|
|
5291 |
(e)f(the)289 3695 y(man)o(y)24 b(equations.)g(This)g(is)g(pretty)g
|
|
5292 |
(much)h(routine.)83 4063 y Fs(4)100 b(Explanation)25
|
|
5293 |
b(and)h(comparison)83 4360 y Fo(4.1)100 b(Repr)l(esentable)24
|
|
5294 |
b(polycate)l(gories)83 4658 y Fr(W)-8 b(e)27 b(recall)g(the)f
|
|
5295 |
(relationship)f(between)h Fn(\003)p Fr(-polycate)o(gories)f(and)i
|
|
5296 |
Fn(\003)p Fr(-autonomous)d(cate)o(gories)i(\(see)83 4778
|
|
5297 |
y([2])e(or)f([11])g(for)g(e)o(xample\).)f(T)-8 b(ak)o(e)23
|
|
5298 |
b(the)g(ob)o(vious)e Fm(2)p Fr(-cate)o(gories)38 b Fn(\003)15
|
|
5299 |
b Fb(P)m(oly)23 b Fr(of)g Fn(\003)p Fr(-polycate)o(gories)f(and)83
|
|
5300 |
4898 y Fn(\003)p Fb(Aut)29 b Fr(of)g Fn(\003)p Fr(-autonomous)f(cate)o
|
|
5301 |
(gories:)g(all)h Fm(2)p Fr(-cells)g(are)h(in)l(v)o(ertible)e(so)h(we)h
|
|
5302 |
(are)g(in)f(the)g(groupoid)83 5019 y(enriched)38 b(setting.)e(An)o(y)h
|
|
5303 |
Fn(\003)p Fr(-autonomous)e(cate)o(gory)i(determines)g(a)g
|
|
5304 |
Fn(\003)p Fr(-polycate)o(gory)-6 b(,)36 b(with)h(the)83
|
|
5305 |
5139 y(linear)c(tensor)f(and)h(par)g(representing)f(polymaps;)f(so)i
|
|
5306 |
(one)f(sees)h(that)f(there)h(is)g(a)g(groupoid)e(en-)83
|
|
5307 |
5259 y(riched)h(for)n(getful)g(functor)f Fq(S)6 b(P)14
|
|
5308 |
b(ol)r(y)43 b Fm(:)d Fn(\003)p Fb(Aut)g Fn(!)g(\003)p
|
|
5309 |
Fb(P)m(oly)p Fr(.)32 b(On)f(the)h(other)f(hand)g(one)h(can)g(freely)83
|
|
5310 |
5380 y(construct)e(a)h Fn(\003)p Fr(-autonomous)e(cate)o(gory)h
|
|
5311 |
(generated)h(by)g(a)f Fn(\003)p Fr(-polycate)o(gory)-6
|
|
5312 |
b(,)29 b(subject)h(to)g(ob)o(vious)p 0 TeXcolorgray 1748
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|
5313 |
5712 a(20)p 0 TeXcolorgray eop end
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|
5314 |
%%Page: 21 21
|
|
5315 |
TeXDict begin 21 20 bop 0 TeXcolorgray 0 TeXcolorgray
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|
5316 |
0 TeXcolorgray 83 83 a Fr(identi\002cations.)27 b(This)g(gi)n(v)o(es)g
|
|
5317 |
(a)h(groupoid)f(enriched)i(functor)f Fq(S)6 b(Aut)33
|
|
5318 |
b Fm(:)h Fn(\003)p Fb(P)m(oly)g Fn(!)g(\003)p Fb(Aut)27
|
|
5319 |
b Fr(and)h(a)83 203 y(groupoid)i(enriched)i(adjunction)d
|
|
5320 |
Fq(S)6 b(Aut)39 b Fn(a)h Fq(S)6 b(P)14 b(ol)r(y)r Fr(.)31
|
|
5321 |
b(The)g(basic)g(conserv)n(ati)n(vity)e(result)i(pro)o(v)o(ed)83
|
|
5322 |
324 y(by)22 b(direct)g(syntactic)f(considerations)g(in)h([2])g
|
|
5323 |
(\(though)f(see)h([11])h(for)f(an)g(indication)f(of)h(a)g(semantic)83
|
|
5324 |
444 y(proof\))j(is)g(as)f(follo)n(ws.)p 0 TeXcolorgray
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|
5325 |
83 620 a Fs(Theor)n(em)j(4.1.)p 0 TeXcolorgray 41 w Fo(In)e(the)f(gr)l
|
|
5326 |
(oupoid)f(enric)o(hed)h(adjunction)f Fq(S)6 b(Aut)28
|
|
5327 |
b Fn(a)f Fq(S)6 b(P)14 b(ol)r(y)s Fo(,)24 b(the)h(unit)1366
|
|
5328 |
840 y Fn(P)37 b(!)27 b Fq(S)6 b(P)14 b(ol)r(y)r(S)6 b(Aut)p
|
|
5329 |
Fm(\()p Fn(P)i Fm(\))83 1060 y Fo(is)25 b(full)f(and)g(faithful)f(for)h
|
|
5330 |
(any)h Fn(\003)p Fo(-polycate)l(gory)f Fn(P)8 b Fo(.)83
|
|
5331 |
1236 y Fr(When)29 b(does)f(a)h Fn(\003)p Fr(-polycate)o(gory)e
|
|
5332 |
Fn(P)37 b Fr(arise)29 b(from)f(a)h Fn(\003)p Fr(-autonomous)d(cate)o
|
|
5333 |
(gory)-6 b(,)28 b(that)g(is)g(when)g(is)g(it)83 1356
|
|
5334 |
y(in)d(the)f(essential)g(image)h(of)g Fq(S)6 b(P)14 b(ol)r(y)t
|
|
5335 |
Fr(?)23 b(This)h(occurs)h(just)f(when)h(there)g(are)h(maps)305
|
|
5336 |
1612 y Fq(i)338 1627 y Fk(A;B)499 1612 y Fm(:)h Fq(A;)17
|
|
5337 |
b(B)33 b Fn(!)27 b Fq(A)c Fn(^)f Fq(B)39 b(i)1234 1627
|
|
5338 |
y Fl(>)1321 1612 y Fm(:)27 b Fn(\000)i(!)e(>)237 b Fq(i)1955
|
|
5339 |
1627 y Fk(C)q(;D)2117 1612 y Fm(:)28 b Fq(C)h Fn(_)23
|
|
5340 |
b Fq(D)30 b Fn(!)d Fq(C)r(;)17 b(D)35 b(i)2863 1627 y
|
|
5341 |
Fl(?)2950 1612 y Fm(:)28 b Fn(?)g(!)g(\000)83 1843 y
|
|
5342 |
Fr(composition)23 b(with)h(which)g(induces)h(isomorphisms)525
|
|
5343 |
2099 y Fn(P)8 b Fm(\()p Fq(A)22 b Fn(^)h Fq(B)5 b(;)17
|
|
5344 |
b Fm(\000;)g(\001\))1198 2072 y Fn(\030)1199 2103 y Fm(=)1304
|
|
5345 |
2099 y Fn(P)8 b Fm(\()p Fq(A;)17 b(B)5 b(;)17 b Fm(\000;)g(\001\))241
|
|
5346 |
b Fn(P)8 b Fm(\()p Fn(>)p Fq(;)17 b Fm(\000;)g(\001\))2613
|
|
5347 |
2072 y Fn(\030)2613 2103 y Fm(=)2718 2099 y Fn(P)8 b
|
|
5348 |
Fm(\(\000;)17 b(\001\))g Fq(;)519 2280 y Fn(P)8 b Fm(\(\000;)17
|
|
5349 |
b(\001)p Fq(;)g(C)29 b Fn(_)23 b Fq(D)s Fm(\))1201 2252
|
|
5350 |
y Fn(\030)1202 2284 y Fm(=)1306 2280 y Fn(P)8 b Fm(\(\000;)17
|
|
5351 |
b(\001)p Fq(;)g(C)r(;)g(D)s Fm(\))249 b Fn(P)8 b Fm(\(\000;)17
|
|
5352 |
b(\001)g Fn(?)p Fm(\))2599 2252 y Fn(\030)2600 2284 y
|
|
5353 |
Fm(=)2704 2280 y Fn(P)8 b Fm(\(\000;)17 b(\001\))g Fq(:)83
|
|
5354 |
2517 y Fr(In)34 b(particular)f(for)g(an)o(y)g Fm(\000)p
|
|
5355 |
Fr(,)g Fm(\001)h Fr(we)g(ha)n(v)o(e)f(isomorphisms)d
|
|
5356 |
Fn(C)6 b Fm(\(\000;)17 b(\001\))2498 2489 y Fn(\030)2498
|
|
5357 |
2521 y Fm(=)2618 2517 y Fn(C)6 b Fm(\()2714 2451 y Ff(V)2800
|
|
5358 |
2517 y Fm(\000;)2905 2451 y Ff(W)2991 2517 y Fm(\001\))33
|
|
5359 |
b Fr(where)h(we)83 2637 y(write)322 2571 y Ff(V)408 2637
|
|
5360 |
y Fm(\000)g Fr(and)681 2571 y Ff(W)767 2637 y Fm(\001)g
|
|
5361 |
Fr(for)g(a)h(conjunction)d(and)i(disjunction)e(according)i(to)g(some)f
|
|
5362 |
(brack)o(etings.)83 2758 y(In)i(these)g(circumstances)f(we)i(say)e
|
|
5363 |
(that)h Fq(i)1577 2773 y Fk(A;B)1710 2758 y Fr(,)g Fq(i)1803
|
|
5364 |
2773 y Fl(>)1862 2758 y Fr(,)g Fq(i)1955 2773 y Fk(C)q(;D)2125
|
|
5365 |
2758 y Fr(and)g Fq(i)2337 2773 y Fl(?)2431 2758 y Fo(pr)l(o)o(vide)f(a)
|
|
5366 |
h(r)l(epr)l(esentation)f(of)83 2878 y(polymaps)p Fr(,)24
|
|
5367 |
b(or)h(more)g(loosely)e(that)i Fn(^)p Fo(,)g Fn(>)p Fo(,)g
|
|
5368 |
Fn(_)p Fo(,)g Fn(?)h Fo(r)l(epr)l(esent)f(polymaps)p
|
|
5369 |
Fr(.)83 3175 y Fo(4.2)100 b(Repr)l(esentability)23 b(and)h
|
|
5370 |
(functoriality)83 3471 y Fr(Consider)j(no)n(w)g(a)g Fn(\003)p
|
|
5371 |
Fr(-polycate)o(gorical)f(model)h Fn(C)33 b Fr(for)28
|
|
5372 |
b(classical)e(proof:)h(it)g(comes)g(equipped)f(with)83
|
|
5373 |
3591 y(structure)805 3712 y Fq(i)838 3727 y Fk(A;B)999
|
|
5374 |
3712 y Fm(=)i Fq(i)1136 3727 y Fk(A)p Fl(^)p Fk(B)1313
|
|
5375 |
3712 y Fq(;)117 b(i)1490 3727 y Fl(>)1577 3712 y Fm(=)27
|
|
5376 |
b Fq(?)17 b(;)116 b(i)1922 3727 y Fk(C)q(;D)2084 3712
|
|
5377 |
y Fm(=)28 b Fq(i)2221 3727 y Fk(C)5 b Fl(_)p Fk(C)2399
|
|
5378 |
3712 y Fq(;)116 b(i)2575 3727 y Fl(?)2662 3712 y Fm(=)28
|
|
5379 |
b Fq(?)83 3862 y Fr(\(using)c(earlier)i(notation\))d(potentially)g(pro)
|
|
5380 |
o(viding)g(a)i(representation)g(of)g(polymaps.)83 4037
|
|
5381 |
y(From)i(our)f(outline)g(of)h(the)f(reconstruction)g(of)h(the)f
|
|
5382 |
Fn(\003)p Fr(-polycate)o(gory)-6 b(,)25 b(we)i(see)g(that)f(we)h(ha)n
|
|
5383 |
(v)o(e)f(rep-)83 4157 y(resentability)e(just)g(when)g(the)h(canonical)g
|
|
5384 |
(linear)f(idempotents)600 4378 y Fq(e)645 4393 y Fk(A)p
|
|
5385 |
Fl(^)p Fk(B)834 4378 y Fm(=)p 937 4302 167 4 v 27 w Fq(i)970
|
|
5386 |
4393 y Fk(A;B)1120 4378 y Fq(;)117 b(e)1309 4393 y Fl(>)1396
|
|
5387 |
4378 y Fm(=)27 b(\()p Fq(i)1570 4393 y Fl(>)1629 4378
|
|
5388 |
y Fm(\))1667 4337 y Fw(+)1743 4378 y Fq(;)116 b(e)1931
|
|
5389 |
4393 y Fk(C)5 b Fl(_)p Fk(D)2125 4378 y Fm(=)p 2229 4302
|
|
5390 |
168 4 v 28 w Fq(i)2262 4393 y Fk(C)q(;D)2413 4378 y Fq(;)117
|
|
5391 |
b(e)2602 4393 y Fl(?)2689 4378 y Fm(=)27 b(\()p Fq(i)2863
|
|
5392 |
4393 y Fl(?)2922 4378 y Fm(\))2960 4337 y Fw(+)83 4598
|
|
5393 |
y Fr(are)f(in)e(f)o(act)h(identities.)e(By)i(duality)-6
|
|
5394 |
b(,)23 b(we)i(only)f(need)h(half)g(of)g(this)e(so)i(representability)e
|
|
5395 |
(is)i(equi)n(v)n(a-)83 4719 y(lent)g(to)f(the)h(conditions)1047
|
|
5396 |
4939 y Fq(e)1092 4954 y Fl(>)1178 4939 y Fm(=)j(id)1363
|
|
5397 |
4954 y Fl(>)1522 4939 y Fr(and)99 b Fm(id)1847 4954 y
|
|
5398 |
Fk(A)1926 4939 y Fn(^)22 b Fm(id)2096 4954 y Fk(B)2184
|
|
5399 |
4939 y Fm(=)28 b(id)2369 4954 y Fk(A)p Fl(^)p Fk(B)2546
|
|
5400 |
4939 y Fq(:)83 5159 y Fr(Ne)o(xt)c(note)h(that,)f(as)h
|
|
5401 |
Fn(^)g Fr(is)g(guarded)g(domain)e(absorbing,)h(we)h(ha)n(v)o(e)779
|
|
5402 |
5380 y Fq(f)33 b Fn(^)23 b Fq(g)t Fm(;)17 b Fq(h)k Fn(^)i
|
|
5403 |
Fq(k)s Fm(;)17 b(id)1389 5395 y Fk(E)1471 5380 y Fn(^)22
|
|
5404 |
b Fm(id)1640 5395 y Fk(F)1727 5380 y Fm(=)27 b(\()p Fq(f)11
|
|
5405 |
b Fm(;)17 b Fq(h)p Fm(\))22 b Fn(^)g Fm(\()p Fq(h)p Fm(;)17
|
|
5406 |
b Fq(k)s Fm(\);)g(id)2530 5395 y Fk(E)2612 5380 y Fn(^)22
|
|
5407 |
b Fm(id)2782 5395 y Fk(F)p 0 TeXcolorgray 1748 5712 a
|
|
5408 |
Fr(21)p 0 TeXcolorgray eop end
|
|
5409 |
%%Page: 22 22
|
|
5410 |
TeXDict begin 22 21 bop 0 TeXcolorgray 0 TeXcolorgray
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|
5411 |
0 TeXcolorgray 83 83 a Fr(so)25 b(that)f Fm(id)452 98
|
|
5412 |
y Fk(E)534 83 y Fn(^)f Fm(id)704 98 y Fk(F)790 83 y Fm(=)28
|
|
5413 |
b(id)975 98 y Fk(E)t Fl(^)p Fk(F)1161 83 y Fr(gi)n(v)o(es)1215
|
|
5414 |
303 y Fq(f)k Fn(^)23 b Fq(g)t Fm(;)17 b Fq(h)k Fn(^)i
|
|
5415 |
Fq(k)31 b Fm(=)c(\()p Fq(f)11 b Fm(;)17 b Fq(h)p Fm(\))22
|
|
5416 |
b Fn(^)g Fm(\()p Fq(h)p Fm(;)17 b Fq(k)s Fm(\))83 524
|
|
5417 |
y Fr(which)22 b(is)f(functoriality)g(of)g Fn(^)p Fr(.)i(One)f(should)e
|
|
5418 |
(re)o(gard)i Fq(e)1965 539 y Fl(>)2052 524 y Fm(=)27
|
|
5419 |
b(id)2236 539 y Fl(>)2317 524 y Fr(as)22 b(functoriality)f(of)h
|
|
5420 |
Fn(>)p Fr(.)g(Then)g(one)83 644 y(can)k(summarise)d(the)i(discussion)e
|
|
5421 |
(in)h(the)h(follo)n(wing.)p 0 TeXcolorgray 83 820 a Fs(Theor)n(em)i
|
|
5422 |
(4.2.)p 0 TeXcolorgray 41 w Fo(Let)e Fn(C)31 b Fo(be)25
|
|
5423 |
b(a)g(model)f(for)g(classical)g(pr)l(oof)o(.)f(Then)i(the)g(following)e
|
|
5424 |
(ar)l(e)i(equivalent.)p 0 TeXcolorgray 123 995 a(\(1\))p
|
|
5425 |
0 TeXcolorgray 50 w(The)h(identity)d(conditions)g Fm(id)1309
|
|
5426 |
1010 y Fk(A)1388 995 y Fn(^)f Fm(id)1558 1010 y Fk(B)1646
|
|
5427 |
995 y Fm(=)28 b(id)1831 1010 y Fk(A)p Fl(^)p Fk(B)2016
|
|
5428 |
995 y Fo(and)d Fq(e)2236 1010 y Fl(>)2323 995 y Fm(=)i(id)2507
|
|
5429 |
1010 y Fl(>)2567 995 y Fo(.)p 0 TeXcolorgray 123 1115
|
|
5430 |
a(\(2\))p 0 TeXcolorgray 50 w(Full)d(functoriality)f(of)h
|
|
5431 |
Fn(^)p Fo(,)h(and)g Fn(>)p Fo(.)p 0 TeXcolorgray 123
|
|
5432 |
1236 a(\(3\))p 0 TeXcolorgray 50 w(Repr)l(esentability)f(of)g(polymaps)
|
|
5433 |
g(by)h Fn(^)p Fo(,)g Fn(>)g Fo(and)g Fn(_)p Fo(,)g Fn(?)p
|
|
5434 |
Fo(.)83 1411 y Fr(This)39 b(mak)o(es)g(clear)g(the)g(o)o(v)o(ersight)e
|
|
5435 |
(in)i([11].)g(There)h(linear)f(maps)f(were)i(assumed)f(to)f(form)h(a)83
|
|
5436 |
1531 y Fn(\003)p Fr(-autonomous)29 b(cate)o(gory;)h(b)n(ut)g(that)h(gi)
|
|
5437 |
n(v)o(es)e Fm(id)1739 1546 y Fk(A)1823 1531 y Fn(^)e
|
|
5438 |
Fm(id)1997 1546 y Fk(B)2096 1531 y Fm(=)39 b(id)2292
|
|
5439 |
1546 y Fk(A)p Fl(^)p Fk(B)2483 1531 y Fr(and)31 b(so)f(functoriality)g
|
|
5440 |
(of)h(the)83 1652 y(logical)21 b(operators.)f(Note)h(also)g(that)f(the)
|
|
5441 |
h(condition)e Fq(f)g Fn(^)8 b Fq(g)t Fm(;)17 b Fq(h)8
|
|
5442 |
b Fn(^)g Fq(k)30 b Fm(=)e(\()p Fq(f)11 b Fm(;)17 b Fq(h)p
|
|
5443 |
Fm(\))8 b Fn(^)g Fm(\()p Fq(h)p Fm(;)17 b Fq(k)s Fm(\))j
|
|
5444 |
Fr(follo)n(ws)g(from)83 1772 y(that)g(naturality)e(of)i(the)g
|
|
5445 |
Fn(^)p Fr(-R)h(rule)f(which)f(we)h(did)f(not)g(adopt.)g(Ho)n(we)n(v)o
|
|
5446 |
(er)g(that)g(condition)f(is)i(weak)o(er)83 1892 y(than)k(full)f
|
|
5447 |
(functoriality)-6 b(.)22 b(It)h(is)h(easy)g(to)f(\002nd)h(models)f(in)g
|
|
5448 |
(which)g(it)g(holds)g(b)n(ut)g Fm(id)2862 1907 y Fk(A)2937
|
|
5449 |
1892 y Fn(^)18 b Fm(id)3103 1907 y Fk(B)3191 1892 y Fm(=)28
|
|
5450 |
b(id)3376 1907 y Fk(A)p Fl(^)p Fk(B)83 2013 y Fr(f)o(ails.)83
|
|
5451 |
2309 y Fo(4.3)100 b(Why)24 b(functoriality)f(should)h(fail)83
|
|
5452 |
2605 y Fr(As)h(we)g(shall)f(see)h(the)f(assumption)f(of)i
|
|
5453 |
(representability)e(pro)o(vides)g(a)i(substantial)e(simpli\002cation)83
|
|
5454 |
2726 y(of)i(the)g(notion)e(of)i(cate)o(gorical)g(model.)f(So)h(it)f(is)
|
|
5455 |
g(time)h(to)f(e)o(xplain)g(why)g(we)h(do)f(not)g(adopt)h(it.)83
|
|
5456 |
2901 y(First)g(we)g(ar)n(gue)g(against)f(the)h(tempting)e(naturality)h
|
|
5457 |
(of)h Fn(^)p Fr(-R)1184 3121 y Fn(f)p Fq(u;)17 b(v)t
|
|
5458 |
Fn(g)p Fm(;)g(\()p Fq(f)31 b Fn(\001)22 b Fq(g)t Fm(\))27
|
|
5459 |
b(=)h(\()p Fq(u)p Fm(;)17 b Fq(f)11 b Fm(\))20 b Fn(\001)i
|
|
5460 |
Fm(\()p Fq(v)t Fm(;)17 b Fq(g)t Fm(\))g Fq(:)83 3334
|
|
5461 |
y Fr(Consider)29 b(\002rst)g Fn(f)p Fq(m;)17 b Fm(id)916
|
|
5462 |
3349 y Fk(B)977 3334 y Fn(g)p Fm(;)g(\(id)1190 3349 y
|
|
5463 |
Fk(A)1247 3334 y Fq(;)g Fm(id)1372 3349 y Fk(B)1432 3334
|
|
5464 |
y Fm(\))p Fr(.)29 b(Composing)f(with)g Fm(id)2300 3349
|
|
5465 |
y Fk(B)2390 3334 y Fr(does)g(nothing)g(so)g(this)g(is)h(equal)83
|
|
5466 |
3447 y(to)c Fq(m)p Fm(;)17 b(\(id)434 3462 y Fk(A)491
|
|
5467 |
3447 y Fq(;)g Fm(id)616 3462 y Fk(B)677 3447 y Fm(\))p
|
|
5468 |
Fr(,)24 b(which)h(is)f(represented)h(by)g(the)f(proof)1183
|
|
5469 |
3635 y Fj(A)i Fh(`)f Fj(A)91 b(A)25 b Fh(`)g Fj(A)p 1183
|
|
5470 |
3655 576 4 v 1211 3735 a(A)20 b Fh(_)g Fj(A)26 b Fh(`)f
|
|
5471 |
Fj(A;)15 b(A)p 1211 3773 521 4 v 1265 3852 a(A)21 b Fh(_)f
|
|
5472 |
Fj(A)25 b Fh(`)g Fj(A)1850 3753 y(A)g Fh(`)g Fj(A)91
|
|
5473 |
b(B)30 b Fh(`)25 b Fj(B)p 1850 3773 587 4 v 1878 3852
|
|
5474 |
a(A;)15 b(B)30 b Fh(`)25 b Fj(A)20 b Fh(^)g Fj(B)p 1265
|
|
5475 |
3890 1144 4 v 1487 3970 a(A)g Fh(_)g Fj(A;)15 b(B)31
|
|
5476 |
b Fh(`)24 b Fj(A)d Fh(^)f Fj(B)1247 b Ft(\(1\))83 4175
|
|
5477 |
y Fr(There)26 b(are)f(tw)o(o)f(distinct)g(w)o(ays)g(to)h(eliminate)f
|
|
5478 |
(the)g(Cut.)h(One)g(results)f(in)g(the)h(normal)f(form)1350
|
|
5479 |
4359 y Fj(A)h Fh(`)g Fj(A)91 b(A)26 b Fh(`)f Fj(A)p 1350
|
|
5480 |
4379 576 4 v 1378 4459 a(A)20 b Fh(_)g Fj(A)25 b Fh(`)g
|
|
5481 |
Fj(A;)15 b(A)p 1378 4497 521 4 v 1432 4576 a(A)20 b Fh(_)g
|
|
5482 |
Fj(A)26 b Fh(`)f Fj(A)173 b(B)29 b Fh(`)c Fj(B)p 1432
|
|
5483 |
4596 838 4 v 1501 4676 a(A)20 b Fh(_)g Fj(A;)15 b(B)30
|
|
5484 |
b Fh(`)25 b Fj(A)c Fh(^)e Fj(B)1234 b Ft(\(2\))83 4881
|
|
5485 |
y Fr(and)25 b(the)g(other)f(in)h(the)f(normal)h(form)1178
|
|
5486 |
5045 y Fj(A)g Fh(`)g Fj(A)91 b(B)30 b Fh(`)25 b Fj(B)p
|
|
5487 |
1178 5065 587 4 v 1206 5145 a(A;)15 b(B)30 b Fh(`)25
|
|
5488 |
b Fj(A)20 b Fh(^)g Fj(B)1855 5045 y(A)26 b Fh(`)f Fj(A)91
|
|
5489 |
b(B)29 b Fh(`)c Fj(B)p 1855 5065 V 1883 5145 a(A;)15
|
|
5490 |
b(B)30 b Fh(`)25 b Fj(A)c Fh(^)e Fj(B)p 1206 5183 1209
|
|
5491 |
4 v 1261 5262 a(A)i Fh(_)f Fj(A;)15 b(B)5 b(;)15 b(B)30
|
|
5492 |
b Fh(`)25 b Fj(A)20 b Fh(^)g Fj(B)5 b(;)15 b(A)20 b Fh(^)g
|
|
5493 |
Fj(B)p 1261 5300 1098 4 v 1460 5380 a(A)g Fh(_)g Fj(A;)15
|
|
5494 |
b(B)30 b Fh(`)25 b Fj(A)c Fh(^)e Fj(B)1275 b Ft(\(3\))p
|
|
5495 |
0 TeXcolorgray 1748 5712 a Fr(22)p 0 TeXcolorgray eop
|
|
5496 |
end
|
|
5497 |
%%Page: 23 23
|
|
5498 |
TeXDict begin 23 22 bop 0 TeXcolorgray 0 TeXcolorgray
|
|
5499 |
0 TeXcolorgray 83 83 a Fr(No)n(w)22 b(consider)g Fm(\()p
|
|
5500 |
Fq(m)p Fm(;)17 b(id)905 98 y Fk(A)962 83 y Fm(\))12 b
|
|
5501 |
Fn(\001)g Fm(\(id)1171 98 y Fk(B)1232 83 y Fm(;)17 b(id)1357
|
|
5502 |
98 y Fk(B)1417 83 y Fm(\))p Fr(.)22 b(This)g(is)f(clearly)i(equal)f(to)
|
|
5503 |
f Fq(m)12 b Fn(\001)g Fm(id)2640 98 y Fk(B)2723 83 y
|
|
5504 |
Fr(which)22 b(is)f(represented)83 203 y(by)i(the)f(\002rst)g(of)h(the)f
|
|
5505 |
(abo)o(v)o(e)g(tw)o(o)g(normal)g(forms.)f(There)i(is)f(no)h(w)o(ay)f
|
|
5506 |
(to)g(get)g(at)h(the)f(second)g(\(though)83 324 y(that)i(is)f(the)h
|
|
5507 |
(normal)f(form)h(in)g(which)f Fq(m)i Fr(has)e(done)h(its)f(intended)g
|
|
5508 |
(job)h(of)g(cop)o(ying\).)f(No)n(w)g(we)h(tak)o(e)83
|
|
5509 |
444 y(the)k(vie)n(w)e(that)h(f)o(ailure)h(to)f(ha)n(v)o(e)g(the)g(same)
|
|
5510 |
h(normal)e(forms)h(\(e)n(v)o(en)g(modulo)f(ob)o(vious)g(re)n
|
|
5511 |
(writings\))83 565 y(is)f(a)g(clear)g(sign)f(of)h(non-identity)-6
|
|
5512 |
b(.)23 b(W)-8 b(e)25 b(conclude)f(that)h(the)f(naturality)g(equation)
|
|
5513 |
914 786 y Fn(f)p Fq(m;)17 b Fm(id)1174 801 y Fk(B)1235
|
|
5514 |
786 y Fn(g)p Fm(;)g(\(id)1447 801 y Fk(A)1526 786 y Fn(\001)22
|
|
5515 |
b Fm(id)1658 801 y Fk(B)1718 786 y Fm(\))28 b(=)f(\()p
|
|
5516 |
Fq(m)p Fm(;)17 b(id)2136 801 y Fk(A)2193 786 y Fm(\))22
|
|
5517 |
b Fn(\001)g Fm(\(id)2422 801 y Fk(B)2482 786 y Fm(;)17
|
|
5518 |
b(id)2607 801 y Fk(B)2668 786 y Fm(\))83 1008 y Fr(is)25
|
|
5519 |
b(not)f(f)o(aithful)g(to)h(the)f(notion)g(of)h(proof)f(encapsulated)h
|
|
5520 |
(in)f(the)h(sequent)f(calculus.)83 1184 y(W)-8 b(e)26
|
|
5521 |
b(e)o(xplain)e(the)i(signi\002cance)f(of)h(this)e(for)i(the)f
|
|
5522 |
(functoriality)f(of)h Fn(^)p Fr(.)h(Consider)g Fm(id)2982
|
|
5523 |
1199 y Fk(A)3061 1184 y Fn(^)d Fm(id)3232 1199 y Fk(B)3292
|
|
5524 |
1184 y Fr(.)j(Note)83 1304 y(that)271 1526 y Fm(\()p
|
|
5525 |
Fq(m)d Fn(^)f Fm(id)586 1541 y Fk(B)647 1526 y Fm(\);)17
|
|
5526 |
b(\(id)848 1541 y Fk(A)927 1526 y Fn(^)23 b Fm(id)1097
|
|
5527 |
1541 y Fk(B)1158 1526 y Fm(\))k(=)p 1327 1441 843 4 v
|
|
5528 |
28 w Fn(f)p Fq(m;)17 b Fm(id)1587 1541 y Fk(B)1647 1526
|
|
5529 |
y Fn(g)p Fm(;)g(\(id)1860 1541 y Fk(A)1939 1526 y Fn(\001)22
|
|
5530 |
b Fm(id)2070 1541 y Fk(B)2131 1526 y Fm(\))100 b(and)f
|
|
5531 |
Fq(m)23 b Fn(^)f Fm(id)2803 1541 y Fk(B)2891 1526 y Fm(=)p
|
|
5532 |
2995 1447 300 4 v 28 w Fq(m)g Fn(\001)g Fm(id)3233 1541
|
|
5533 |
y Fk(B)3322 1526 y Fq(:)83 1748 y Fr(No)n(w)i(we)i(just)d(ar)n(gued)j
|
|
5534 |
(that)e(we)h(should)f(not)g(ha)n(v)o(e)1146 1970 y Fn(f)p
|
|
5535 |
Fq(m;)17 b Fm(id)1406 1985 y Fk(B)1467 1970 y Fn(g)p
|
|
5536 |
Fm(;)g(\(id)1680 1985 y Fk(A)1759 1970 y Fn(\001)22 b
|
|
5537 |
Fm(id)1890 1985 y Fk(B)1951 1970 y Fm(\))27 b(=)h Fq(m)22
|
|
5538 |
b Fn(\001)g Fm(id)2358 1985 y Fk(B)2447 1970 y Fq(:)83
|
|
5539 |
2191 y Fr(But)j(as)g Fq(i)393 2206 y Fk(A)p Fl(^)p Fk(B)554
|
|
5540 |
2191 y Fm(;)p 598 2112 57 4 v 17 w Fq(h)i Fm(=)h Fq(h)p
|
|
5541 |
Fr(,)d(the)g(operation)p 1439 2107 104 4 v 24 w Fm(\()i(\))e
|
|
5542 |
Fr(is)g(injecti)n(v)o(e.)e(So)i(we)g(cannot)f(ha)n(v)o(e)h(the)f
|
|
5543 |
(equation)1086 2413 y Fm(\()p Fq(m)e Fn(^)h Fm(id)1401
|
|
5544 |
2428 y Fk(B)1462 2413 y Fm(\);)17 b(\(id)1662 2428 y
|
|
5545 |
Fk(A)1742 2413 y Fn(^)22 b Fm(id)1911 2428 y Fk(B)1972
|
|
5546 |
2413 y Fm(\))28 b(=)f Fq(m)c Fn(^)f Fm(id)2419 2428 y
|
|
5547 |
Fk(B)2507 2413 y Fq(:)83 2635 y Fr(The)32 b(general)g(point)e(seems)h
|
|
5548 |
(to)g(be)h(this.)e(If)i(we)g(cut)f(a)h(classical)f(proof)g(e)n(v)o(en)g
|
|
5549 |
(with)g(such)g(simple)83 2755 y(proofs)j(as)h(gi)n(v)o(en)e(by)h(our)h
|
|
5550 |
(canonical)f(linear)g(idempotents,)f(then)h(we)h(can,)g(in)f(general,)g
|
|
5551 |
(obtain)83 2876 y(additional)24 b(normal)g(forms)g(that)h(were)g(not)f
|
|
5552 |
(a)n(v)n(ailable)g(from)h(the)g(classical)f(proof)h(on)f(its)g(o)n(wn.)
|
|
5553 |
83 3176 y Fo(4.4)100 b(F)377 3177 y(\250)369 3176 y(uhrmann-Pym)23
|
|
5554 |
b(Axioms)83 3472 y Fr(W)-8 b(e)31 b(observ)o(ed)f(already)g(that)g(a)h
|
|
5555 |
Fn(\003)p Fr(-polycate)o(gory)e(in)h(which)g(the)g(polymaps)f(are)i
|
|
5556 |
(represented)g(by)83 3592 y Fn(^)c Fr(and)f Fn(_)h Fr(is)e(in)h(ef)n
|
|
5557 |
(fect)g(a)h Fn(\003)p Fr(-autonomous)d(cate)o(gory)-6
|
|
5558 |
b(.)25 b(If)i(one)f(has)g(a)g(model)f(for)i(classical)e(proof)h(of)83
|
|
5559 |
3713 y(this)e(kind)g(the)h(structure)f(simpli\002es)g(drastically)-6
|
|
5560 |
b(.)p 0 TeXcolorgray 83 3889 a Fs(Theor)n(em)36 b(4.3.)p
|
|
5561 |
0 TeXcolorgray 46 w Fo(T)-9 b(o)34 b(give)g(a)f(model)h(of)f(classical)
|
|
5562 |
g(pr)l(oof)f(in)h(whic)o(h)h Fn(^)p Fo(,)g Fn(>)h Fo(and)e
|
|
5563 |
Fn(_)p Fo(,)h Fn(?)g Fo(r)l(epr)l(esent)83 4009 y(polymaps)24
|
|
5564 |
b(is)g(to)h(give)g(the)f(following)g(data.)p 0 TeXcolorgray
|
|
5565 |
83 4185 a Fn(\017)p 0 TeXcolorgray 50 w Fo(A)h Fn(\003)p
|
|
5566 |
Fo(-autonomous)e(cate)l(gory)h Fa(C)51 b Fo(\(with)25
|
|
5567 |
b(a)g(strict)e(duality\):)h(tensor)g(is)h Fn(^)g Fo(and)f(par)h
|
|
5568 |
Fn(_)p Fo(.)p 0 TeXcolorgray 83 4306 a Fn(\017)p 0 TeXcolorgray
|
|
5569 |
50 w Fo(The)33 b(equipment)e(on)h(eac)o(h)g(object)g
|
|
5570 |
Fq(A)g Fo(of)g Fa(C)58 b Fo(of)32 b(the)g(structur)l(e)f(of)h(a)g
|
|
5571 |
(commutative)f(comonoid)183 4426 y(with)36 b(r)l(espect)f(to)h(tensor)f
|
|
5572 |
(\(and)g(so)h(dually)f(the)g(structur)l(e)g(of)g(a)h(commutative)f
|
|
5573 |
(monoid)g(with)183 4546 y(r)l(espect)25 b(to)f(par\).)83
|
|
5574 |
4722 y Fr(This)h(is)g(the)g(equality)g(component)f(of)h(the)g
|
|
5575 |
(structure)h(proposed)e(in)h(F)8 b(\250)-41 b(uhrmann)25
|
|
5576 |
b(and)h(Pym)f([6].)g(\(It)83 4843 y(is)32 b(not)g(the)g(only)g(simple)f
|
|
5577 |
(possibility)-6 b(.)29 b(W)-8 b(e)32 b(ha)n(v)o(e)g(recently)h(seen)f
|
|
5578 |
(w)o(ork)g([14])g(of)h(Lamarche)g(and)83 4963 y(Strassb)n(ur)n(ger)26
|
|
5579 |
b(which)e(leads)h(to)f(an)h(e)n(v)o(en)f(more)h(restricti)n(v)o(e)e
|
|
5580 |
(notion.\))83 5139 y(There)k(are)h(a)f(number)f(of)h(further)g
|
|
5581 |
(connections)e(between)i(the)f(F)8 b(\250)-41 b(uhrmann-Pym)27
|
|
5582 |
b(notion)e(and)i(the)83 5259 y(one)22 b(described)g(in)g(this)f(paper)
|
|
5583 |
-5 b(.)22 b(One)g(simple)e(thought)h(is)g(as)i(follo)n(ws.)d(Suppose)i
|
|
5584 |
(that)f Fn(C)28 b Fr(is)22 b(a)g(model)83 5380 y(for)f(classical)f
|
|
5585 |
(logic)g(in)g(the)g(general)h(sense,)f(freely)h(generated)f(by)h(some)e
|
|
5586 |
(cate)o(gory)h(of)h(objects)f(and)p 0 TeXcolorgray 1748
|
|
5587 |
5712 a(23)p 0 TeXcolorgray eop end
|
|
5588 |
%%Page: 24 24
|
|
5589 |
TeXDict begin 24 23 bop 0 TeXcolorgray 0 TeXcolorgray
|
|
5590 |
0 TeXcolorgray 83 83 a Fr(maps.)24 b(\(This)f(mak)o(es)h(sense)g(by)g
|
|
5591 |
(K)n(elly-Po)n(wer)g([13].\))g(W)-8 b(e)24 b(can)h(inducti)n(v)o(ely)d
|
|
5592 |
(de\002ne)i(idempotents)83 203 y Fq(e)128 218 y Fk(A)209
|
|
5593 |
203 y Fr(on)f(objects)f Fq(A)i Fr(of)f Fn(C)6 b Fr(:)23
|
|
5594 |
b(we)h(set)e Fq(e)1267 218 y Fk(A)1352 203 y Fm(=)28
|
|
5595 |
b(id)1537 218 y Fk(A)1617 203 y Fr(for)c(atomic)e(objects)h(\(which)g
|
|
5596 |
(includes)f(the)h(duals)g Fq(A)3464 167 y Fl(\003)3503
|
|
5597 |
203 y Fr(\))83 324 y(and)g(then)g(set)g Fq(e)624 339
|
|
5598 |
y Fk(A)p Fl(^)p Fk(B)812 324 y Fm(=)28 b Fq(e)961 339
|
|
5599 |
y Fk(A)1034 324 y Fn(^)16 b Fq(e)1161 339 y Fk(B)1245
|
|
5600 |
324 y Fr(and)23 b Fq(e)1457 339 y Fk(A)p Fl(_)p Fk(B)1646
|
|
5601 |
324 y Fm(=)k Fq(e)1794 339 y Fk(A)1867 324 y Fn(_)16
|
|
5602 |
b Fq(e)1994 339 y Fk(B)2055 324 y Fr(.)23 b(\(Implicitly)f(we)h(ha)n(v)
|
|
5603 |
o(e)g(tak)o(en)g Fq(e)3183 339 y Fl(>)3265 324 y Fr(and)g
|
|
5604 |
Fq(e)3477 339 y Fl(?)83 444 y Fr(as)i(we)g(found)g(them.\))f(Then)h(we)
|
|
5605 |
g(can)g(de\002ne)g(a)g(quotient)2113 419 y Fm(^)2095
|
|
5606 |
444 y Fn(C)31 b Fr(of)25 b Fn(C)31 b Fr(with)963 632
|
|
5607 |
y Fm(^)944 657 y Fn(C)6 b Fm(\()p Fq(A;)17 b(B)5 b Fm(\))28
|
|
5608 |
b(=)g Fn(f)p Fq(f)38 b Fn(2)28 b(C)6 b Fm(\()p Fq(A;)17
|
|
5609 |
b(B)5 b Fm(\))17 b Fn(j)g Fq(e)2073 672 y Fk(A)2129 657
|
|
5610 |
y Fm(;)g Fq(f)11 b Fm(;)17 b Fq(e)2321 672 y Fk(B)2409
|
|
5611 |
657 y Fm(=)27 b Fq(f)11 b Fn(g)27 b Fq(:)83 870 y Fr(The)e(quotient)f
|
|
5612 |
(functor)g(is)h(gi)n(v)o(en)e(by)992 1083 y Fn(C)6 b
|
|
5613 |
Fm(\()p Fq(A;)17 b(B)5 b Fm(\))27 b Fn(\000)-16 b(!)1556
|
|
5614 |
1057 y Fm(^)1538 1083 y Fn(C)6 b Fm(\()p Fq(A;)17 b(B)5
|
|
5615 |
b Fm(\))55 b(:)g Fq(f)39 b Fn(!)27 b Fq(e)2264 1098 y
|
|
5616 |
Fk(A)2321 1083 y Fm(;)17 b Fq(f)11 b Fm(;)17 b Fq(e)2513
|
|
5617 |
1098 y Fk(B)2601 1083 y Fq(:)83 1296 y Fr(No)n(w)22 b(it)f(is)h(easy)g
|
|
5618 |
(to)f(see)i(that)1101 1270 y Fm(^)1082 1296 y Fn(C)29
|
|
5619 |
b Fr(has)21 b(on)h(the)g(nose)g(the)g(structure)f(which)h
|
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