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cleartomark
%%EndFont 
%%BeginFont: CMSL10
%!PS-AdobeFont-1.1: CMSL10 1.0
%%CreationDate: 1991 Aug 20 16:40:20
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSL10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -9.46 def
/isFixedPitch false def
end readonly def
/FontName /CMSL10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 44 /comma put
dup 46 /period put
dup 58 /colon put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 70 /F put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 127 /dieresis put
readonly def
/FontBBox{-62 -250 1123 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 19 /acute put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 75 /K put
dup 84 /T put
readonly def
/FontBBox{0 -504 2615 1004}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: EUFM10
%!PS-AdobeFont-1.1: EUFM10 2.1
%%CreationDate: 1992 Nov 20 17:36:20
% Euler fonts were designed by Hermann Zapf.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (EUFM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EUFM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 76 /L put
dup 112 /p put
readonly def
/FontBBox{-26 -224 1055 741}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 77 /circleplusdisplay put
dup 81 /producttext put
dup 89 /productdisplay put
dup 96 /coproducttext put
dup 98 /hatwide put
dup 101 /tildewide put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /square put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX8
%!PS-AdobeFont-1.1: CMBX8 1.0
%%CreationDate: 1991 Aug 20 16:36:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 70 /F put
dup 71 /G put
dup 77 /M put
dup 79 /O put
dup 82 /R put
dup 83 /S put
dup 99 /c put
dup 101 /e put
dup 102 /f put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 116 /t put
readonly def
/FontBBox{-59 -250 1235 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 77 /M put
dup 86 /V put
dup 88 /X put
dup 97 /a put
dup 107 /k put
dup 111 /o put
dup 112 /p put
readonly def
/FontBBox{11 -250 1241 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 48 /prime put
dup 67 /C put
dup 70 /F put
dup 71 /G put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 75 /K put
dup 78 /N put
dup 81 /Q put
dup 82 /R put
dup 84 /T put
dup 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: LCIRCLE10
%!PS-AdobeFont-1.1: LCIRCLE10 1.001
%%CreationDate: 1992 Oct 23 20:21:59
%%RevisionDate: 2001 Jun 05 20:21:59
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LCIRCLE10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /LCIRCLE10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /a12 put
dup 13 /a13 put
dup 14 /a14 put
dup 15 /a15 put
readonly def
/FontBBox{-2000 -2000 2040 2040}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: LINE10
%!PS-AdobeFont-1.1: LINE10 1.001
%%CreationDate: 1992 Oct 23 20:22:05
%%RevisionDate: 2001 Jun 05 20:22:05
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LINE10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /LINE10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /a0 put
dup 1 /a1 put
dup 8 /a8 put
dup 9 /a9 put
dup 11 /a11 put
dup 16 /a16 put
dup 18 /a18 put
dup 25 /a25 put
dup 27 /a27 put
dup 41 /a41 put
dup 42 /a42 put
dup 45 /a45 put
dup 49 /a49 put
dup 54 /a54 put
dup 63 /a63 put
dup 64 /a64 put
dup 65 /a65 put
dup 72 /a72 put
dup 73 /a73 put
dup 80 /a80 put
dup 81 /a81 put
dup 82 /a82 put
dup 85 /a85 put
dup 88 /a88 put
dup 89 /a89 put
dup 105 /a105 put
dup 106 /a106 put
dup 113 /a113 put
dup 115 /a115 put
dup 122 /a122 put
readonly def
/FontBBox{-150 -150 1020 1020}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 19 /iota put
dup 22 /mu put
dup 24 /xi put
dup 25 /pi put
dup 30 /phi put
dup 32 /psi put
dup 34 /epsilon put
dup 59 /comma put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 10 /circlemultiply put
dup 48 /prime put
dup 50 /element put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 77 /M put
dup 80 /P put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 113 /coproduct put
dup 114 /nabla put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 1 /Delta put
dup 8 /Phi put
dup 33 /exclam put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 65 /A put
dup 69 /E put
dup 77 /M put
dup 78 /N put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 103 /g put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 111 /o put
dup 113 /q put
dup 114 /r put
dup 116 /t put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 12 /beta put
dup 14 /delta put
dup 17 /eta put
dup 19 /iota put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 28 /tau put
dup 30 /phi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 39 /phi1 put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 10 /circlemultiply put
dup 14 /openbullet put
dup 15 /bullet put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 24 /similar put
dup 26 /propersubset put
dup 32 /arrowleft put
dup 33 /arrowright put
dup 40 /arrowdblleft put
dup 41 /arrowdblright put
dup 43 /arrowdbldown put
dup 50 /element put
dup 51 /owner put
dup 54 /negationslash put
dup 55 /mapsto put
dup 56 /universal put
dup 57 /existential put
dup 58 /logicalnot put
dup 59 /emptyset put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 85 /U put
dup 91 /union put
dup 92 /intersection put
dup 94 /logicaland put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 110 /backslash put
dup 113 /coproduct put
dup 114 /nabla put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 13 /fl put
dup 33 /exclam put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 52 /four put
dup 55 /seven put
dup 58 /colon put
dup 59 /semicolon put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-36 -251 1103 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 1 /Delta put
dup 12 /fi put
dup 40 /parenleft put
dup 41 /parenright put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 58 /colon put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 89 /Y put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 89 /Y put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 78 /N put
dup 79 /O put
dup 82 /R put
dup 84 /T put
dup 89 /Y put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
readonly def
/FontBBox{14 -250 1077 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 1 /Delta put
dup 8 /Phi put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 33 /exclam put
dup 34 /quotedblright put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 89 /Y put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-34 -251 988 750}readonly def
currentdict end
currentfile eexec
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%%BeginFont: CMR17
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%%CreationDate: 1991 Aug 20 16:38:24
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 84 /T put
dup 97 /a put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 111 /o put
dup 114 /r put
dup 116 /t put
dup 121 /y put
readonly def
/FontBBox{-33 -250 945 749}readonly def
currentdict end
currentfile eexec
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TeXDict begin 39139632 55387786 1000 600 600
(D:/Backup/wwwpublic/Cats.dvi) @start /Fa 198[48 48 48
48 1[48 1[48 48 48 48[{}8 83.022 /CMBX10 rf /Fb 128[42
5[44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 25 23
46 42 25 37 46 37 46 42 12[60 46 2[57 65 62 1[52 65 1[30
2[54 2[60 59 62 1[39 4[23 11[23 1[23 31[46 12[{}43 83.022
/CMSL10 rf /Fc 133[37 44 2[44 46 32 33 33 44 46 42 46
69 23 44 1[23 46 42 25 37 46 37 46 42 3[23 1[23 3[85
62 62 60 46 61 1[57 1[62 76 52 1[43 30 62 65 54 57 63
60 59 62 6[23 42 42 42 42 1[42 42 42 42 42 1[23 28 23
24[42 19[{}59 83.022 /CMR10 rf /Fd 171[44 8[52 75[{}2
66.4176 /MSBM7 rf /Fe 143[50 35[66 76[{}2 99.6264 /EUFM10
rf /Ff 154[39 101[{}1 66.4176 /CMEX10 rf /Fg 252[77 3[{}1
99.6264 /MSAM10 rf /Fh 154[55 2[55 1[94 6[127 7[94 3[151
75[46 46{}8 99.6264 /CMEX10 rf /Fi 139[32 1[34 2[41 45
1[23 2[23 2[25 37 1[36 15[45 61 2[61 1[77 5[64 51 70[{}15
66.4176 /CMBX8 rf /Fj 205[30 30 30 6[24 24 40[{}5 49.8132
/CMR6 rf /Fk 143[32 31 3[33 9[34 8[50 1[36 8[58 9[44
46 46 65[{}10 49.8132 /CMMI6 rf /Fl 184[37 44 2[34 18[18
47[48{}5 49.8132 /CMSY6 rf /Fm 165[66 5[66 1[72 77 2[72
2[77 75[{}6 99.6264 /MSBM10 rf /Fn 240[133 133 133 133
12[{}4 83.022 /LCIRCLE10 rf /Fo 133[83 6[83 1[83 6[83
83 15[83 83 2[42 2[83 83 83 6[83 83 6[42 83 83 8[83 4[83
3[83 2[83 83 13[83 1[83 6[83 1[83 4[42 1[83 83 6[42 83{}30
83.022 /LINE10 rf /Fp 134[35 40 51 1[41 25 33 32 1[36
34 43 62 1[37 29 24 41 34 34 33 3[37 6[48 41 58 1[41
1[41 43 53 1[45 1[56 68 48 60 1[31 1[55 45 52 58 50 53
53 3[35 1[20 24[33 1[46 1[42 4[41 31 1[42 2[25 7[45 11[{}49
66.4176 /CMMI8 rf /Fq 141[59 53 7[27 27 23[49 2[84 4[60
42 50 1[55 37 16[47 1[19 37[55 6[35 55 20 55{}18 66.4176
/CMSY8 rf /Fr 139[27 1[28 37 1[35 1[59 20 2[20 1[35 3[31
39 35 3[20 1[20 12[53 65 7[48 3[53 13[35 35 35 35 4[55
1[27 27 6[20 24[51 6[59 1[{}27 66.4176 /CMR8 rf /Fs 133[45
48 55 70 47 56 35 46 44 43 49 47 58 85 29 51 40 33 56
47 48 45 51 42 41 51 6[67 57 81 92 57 66 57 60 74 77
63 75 78 94 66 83 54 43 81 77 63 72 81 70 74 73 2[76
49 76 27 27 18[64 4[46 61 63 1[58 1[42 2[55 43 48 59
57 1[34 1[48 2[43 1[55 62 11[{}73 99.6264 /CMMI12 rf
/Ft 141[83 75 2[50 3[28 39 39 50 50 7[66 1[66 66 5[62
4[69 1[82 120 1[76 68 54 84 59 72 53 77 52 65 80 5[50
66 55 55 0 0 2[66 66 6[61 1[100 100 6[100 100 5[77 1[77
2[77 77 1[77 2[50 50 3[77 6[50 77 28 77{}51 99.6264 /CMSY10
rf /Fu 133[40 47 45 65 45 52 32 40 41 45 50 50 55 80
25 45 30 30 50 45 30 45 50 45 45 50 7[72 1[97 1[72 70
55 2[66 75 72 87 61 75 1[38 72 75 64 66 74 70 1[72 5[30
30 2[50 2[50 1[50 50 50 1[30 35 30 1[50 40 40 6[30 19[57
55 12[{}61 99.6264 /CMTI12 rf /Fv 132[56 50 59 59 81
59 62 44 44 46 59 62 56 62 93 31 59 34 31 62 56 34 51
62 50 62 54 7[85 1[116 85 86 78 62 84 84 77 84 88 106
67 88 1[42 88 88 70 74 86 81 80 85 1[53 4[31 6[56 56
56 56 1[31 37 3[44 44 27[62 10[93 1[{}62 99.6264 /CMBX12
rf /Fw 133[34 41 41 1[41 43 30 30 30 41 43 38 43 64 21
1[23 21 43 38 23 34 43 34 43 38 7[58 3[58 55 43 57 1[52
1[58 70 48 2[28 1[60 50 52 1[55 1[58 7[38 38 38 38 38
38 38 38 38 38 48[{}49 74.7198 /CMR9 rf /Fx 138[61 59
46 60 1[56 63 61 74 51 1[42 30 61 1[53 56 62 59 58 61
7[81 4[78 1[80 2[84 81 1[68 2[40 81 1[71 74 1[78 77 81
65[{}31 99.6264 /CMCSC10 rf /Fy 132[49 43 51 51 70 51
54 38 38 38 51 54 49 54 81 27 51 30 27 54 49 30 43 54
43 54 49 27 2[27 49 27 1[73 1[100 73 73 70 54 72 1[66
76 73 89 61 76 50 35 73 77 64 66 75 70 69 73 1[46 1[76
1[27 27 49 49 49 49 49 49 49 49 49 49 1[27 33 27 76 49
38 38 27 76 3[49 27 18[81 54 54 57 2[70 6[81 1[{}85 99.6264
/CMR12 rf /Fz 140[46 46 2[59 5[33 1[59 36 52 3[59 16[80
11[89 1[83 19[33 46[{}12 119.552 /CMR12 rf /FA 134[83
4[61 1[61 2[79 6[88 79 1[70 3[79 12[115 16[115 67[{}10
172.188 /CMR17 rf end
%%EndProlog
%%BeginSetup
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TeXDict begin
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%%Page: 1 1
TeXDict begin 1 0 bop Black Black Black Black 1362 701
a FA(Category)52 b(Theory)1423 1040 y Fz(Prof.)37 b(Dr.)h(B.)h(P)m
(areigis)1454 1285 y Fy(Summer)34 b(Semester)g(2004)1657
1530 y(June)f(14,)f(2004)1709 2570 y Fx(Contents)100
2744 y Fy(In)m(tro)s(duction)3218 b(3)100 2860 y(1.)97
b(F)-8 b(oundations)3056 b(6)100 2976 y(1.1.)97 b(Graphs)3192
b(6)100 3093 y(1.2.)97 b(Monoids)3142 b(8)100 3209 y(1.3.)97
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TeXDict begin 56 55 bop Black 0 -99 a Fw(56)1077 b(Represen)n(table)25
b(functors)h(and)g(the)f(Y)-6 b(oneda)25 b(Lemma)p Black
0 100 a Fy(w)m(e)49 b(get)g Fs(a)55 b Fy(=)f(pro)5 b(j)750
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b(j)3137 124 y Fr(1)3176 100 y Fy(\()p Fs(a)3265 64 y
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217 y Fs(b)49 b Fy(=)f(pro)5 b(j)390 240 y Fr(2)429 217
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240 y Fr(2)1084 217 y Ft(\016)p Fs(h)p Fy(\)\()p Fs(t)p
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217 y Fy(\()p Fs(a)2844 180 y Fq(0)2868 217 y Fs(;)17
b(b)2953 180 y Fq(0)2976 217 y Fy(\))48 b(=)g Fs(b)3227
180 y Fq(0)3251 217 y Fy(,)g(hence)e Fs(h)p Fy(\()p Fs(t)p
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333 y Fy(\))28 b(=)g Fs(k)s Fy(\()p Fs(t)p Fy(\))k(and)h
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565 y Fy(w)m(e)34 b(de\014ne)1465 693 y(\()p Fs(f)5 b(;)17
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Fy(\()p Fs(t)p Fy(\))p Fs(;)17 b(g)t Fy(\()p Fs(t)p Fy(\)\))p
Fs(:)0 841 y Fy(This)23 b(is)f(a)g(map)g(from)f Fs(T)35
b Fy(to)22 b Fs(A)p Ft(\002)p Fs(B)5 b Fy(.)40 b(Since)23
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841 y Ft(\016)p Fy(\()p Fs(f)g(;)17 b(g)t Fy(\)\)\()p
Fs(t)p Fy(\))26 b(=)i Fs(f)11 b Fy(\()p Fs(t)p Fy(\))21
b(and)h(\(pro)5 b(j)3379 864 y Fr(2)3435 841 y Ft(\016)p
Fy(\()p Fs(f)g(;)17 b(g)t Fy(\)\)\()p Fs(t)p Fy(\))27
b(=)0 957 y Fs(g)t Fy(\()p Fs(t)p Fy(\))32 b(w)m(e)i(get)e(pro)5
b(j)676 980 y Fr(1)732 957 y Ft(\016)p Fy(\()p Fs(f)g(;)17
b(g)t Fy(\))27 b(=)g Fs(f)44 b Fy(and)32 b(pro)5 b(j)1594
980 y Fr(2)1650 957 y Ft(\016)p Fy(\()p Fs(f)g(;)17 b(g)t
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b(an)m(y)f(triple)g(\()p Fs(P)s(;)17 b(p)1132 1101 y
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1162 y Fp(B)1864 1137 y Fy(:)46 b Fs(P)60 b Ft(\000)-60
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b Ft(\002)h Fs(B)5 b(;)17 b Fy(pro)5 b(j)3563 1160 y
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1137 y Fy(\))0 1253 y(satis\014es)39 b(the)f(same)h(univ)m(ersal)g
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Fs(B)43 b Fy(b)s(e)38 b(an)f(isomorphism)i(suc)m(h)0
1369 y(that)1910 1456 y Fs(P)1425 1700 y(A)1536 1568
y(p)1585 1532 y Fq(0)1585 1593 y Fp(A)1729 1532 y Fo(\010)1646
1573 y(\010)1598 1598 y(\010)-83 b(\031)2396 1700 y Fs(B)2255
1568 y(p)2304 1532 y Fq(0)2304 1593 y Fp(B)2085 1532
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b Ft(\002)g Fs(B)1427 1809 y Fy(pro)5 b(j)1603 1832 y
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b(Y)2255 1809 y Fy(pro)5 b(j)2431 1832 y Fr(2)2085 1841
y Fo(\010)2168 1800 y(\010)2216 1776 y(\010)-83 b(*)p
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Ft(\000)-59 b(!)48 b Fs(A)p Fy(,)g Fs(g)k Fy(:)d Fs(T)62
b Ft(\000)-60 b(!)48 b Fs(B)i Fy(b)s(e)45 b(maps.)81
b(Then)46 b(the)g(map)0 2174 y Fs(h)56 2137 y Fq(\000)p
Fr(1)170 2174 y Ft(\016)19 b Fy(\()p Fs(f)5 b(;)17 b(g)t
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b Fy(satis\014es)33 b Fs(p)1302 2137 y Fq(0)1302 2199
y Fp(A)1379 2174 y Ft(\016)19 b Fy(\()p Fs(h)1542 2137
y Fq(\000)p Fr(1)1655 2174 y Ft(\016)h Fy(\()p Fs(f)5
b(;)17 b(g)t Fy(\)\))26 b(=)i Fs(f)42 b Fy(and)31 b Fs(p)2444
2137 y Fq(0)2444 2199 y Fp(B)2524 2174 y Ft(\016)19 b
Fy(\()p Fs(h)2687 2137 y Fq(\000)p Fr(1)2801 2174 y Ft(\016)g
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b(An)33 b(ob)5 b(ject)34 b Fs(A)22 b Ft(\002)h Fs(B)38
b Fy(together)33 b(with)0 3284 y(morphisms)e Fs(p)540
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b Ft(\000)-59 b(!)27 b Fs(A)i Fy(and)h Fs(p)1452 3299
y Fp(B)1540 3284 y Fy(:)e Fs(A)16 b Ft(\002)g Fs(B)34
b Ft(\000)-60 b(!)27 b Fs(B)35 b Fy(is)30 b(called)g(a)g(\(not)f
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b(o)g(duct)0 3401 y Fy(of)32 b Fs(A)h Fy(and)h Fs(B)5
b Fy(,)33 b(and)g(the)g(morphisms)i Fs(p)1449 3416 y
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b Ft(C)39 b Fy(there)0 3517 y(is)33 b(an)g(isomorphism)h(of)e(sets)1000
3685 y(Mor)1177 3700 y Fq(C)1222 3685 y Fy(\()p Fs(T)8
b(;)17 b(A)22 b Ft(\002)g Fs(B)5 b Fy(\))1708 3657 y
Ft(\030)1709 3689 y Fy(=)1813 3685 y(Mor)1989 3700 y
Fq(C)2035 3685 y Fy(\()p Fs(T)j(;)17 b(A)p Fy(\))22 b
Ft(\002)g Fy(Mor)2590 3700 y Fq(C)2635 3685 y Fy(\()p
Fs(T)8 b(;)17 b(B)5 b Fy(\))0 3853 y(\(where)34 b(Mor)496
3868 y Fq(C)541 3853 y Fy(\()p Fs(T)8 b(;)17 b(A)p Fy(\))22
b Ft(\002)h Fy(Mor)1097 3868 y Fq(C)1142 3853 y Fy(\()p
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4028 y Fq(C)1830 4013 y Fy(\()p Fs(T)8 b(;)17 b(A)22
b Ft(\002)h Fs(B)5 b Fy(\))539 4403 y(Mor)715 4418 y
Fq(C)760 4403 y Fy(\()p Fs(T)j(;)17 b(A)p Fy(\))787 4208
y(Mor)963 4223 y Fq(C)1008 4208 y Fy(\()p Fs(T)8 b(;)17
b(p)1204 4223 y Fp(A)1261 4208 y Fy(\))1661 4084 y Fo(\020)1578
4112 y(\020)1495 4139 y(\020)1412 4167 y(\020)1329 4195
y(\020)1246 4222 y(\020)1163 4250 y(\020)1080 4278 y(\020)997
4305 y(\020)983 4310 y(\020)-83 b(\))2876 4403 y Fy(Mor)3052
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Fs(T)j(;)17 b(p)3015 4223 y Fp(B)3076 4208 y Fy(\))2153
4084 y Fo(P)2236 4112 y(P)2319 4139 y(P)2402 4167 y(P)2485
4195 y(P)2568 4222 y(P)2651 4250 y(P)2734 4278 y(P)2817
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4617 y(P)1329 4589 y(P)1246 4562 y(P)1163 4534 y(P)1080
4506 y(P)997 4478 y(P)983 4474 y(P)-83 b(i)2598 4579
y Fs(p)2647 4594 y Fr(Mor)2774 4605 y Fl(C)2814 4594
y Fr(\()p Fp(T)6 b(;B)s Fr(\))2153 4700 y Fo(\020)2236
4672 y(\020)2319 4645 y(\020)2402 4617 y(\020)2485 4589
y(\020)2568 4562 y(\020)2651 4534 y(\020)2734 4506 y(\020)2817
4478 y(\020)2831 4474 y(\020)-83 b(1)p 1947 4700 4 644
v 1949 4700 a(?)1988 4413 y Fs(h)0 4939 y Fy(comm)m(utes.)-438
5004 y(11.06.04)p Black 0 5185 a(2.7.4.)32 b Fv(Prop)s(osition)37
b Fy(\()p Fv(Characterization)h(of)g(pro)s(ducts)g(b)m(y)f(the)g(univ)m
(ersal)i(mapping)g(prop-)0 5301 y(ert)m(y\).)p Black
43 w Fu(Given)g(obje)-5 b(cts)38 b Fs(A)h Fu(and)f Fs(B)44
b Fu(in)39 b(a)f(c)-5 b(ate)g(gory)39 b Ft(C)6 b Fu(.)57
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b Ft(\000)-57 b(!)28 b Fs(B)40 b Fu(is)34 b(a)h(\(c)-5
b(ate)g(goric)g(al\))34 b(pr)-5 b(o)g(duct,)p Black Black
eop end
%%Page: 57 57
TeXDict begin 57 56 bop Black 1799 -99 a Fw(Pro)r(ducts)1722
b(57)p Black Black 100 100 a Fy(\(**\))p Black 41 w Fu(if)38
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b Fs(T)49 b Ft(2)35 b(C)45 b Fu(and)38 b(e)-5 b(ach)38
b(p)-5 b(air)38 b(of)h(morphisms)e Fs(f)46 b Fy(:)35
b Fs(T)48 b Ft(\000)-57 b(!)35 b Fs(A)p Fu(,)k Fs(g)f
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b(!)28 b Fs(A)22 b Ft(\002)g Fs(B)40 b Fu(such)35 b(that)g(the)g(diagr)
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1028 y Ft(\016)22 b Fy(\()p Fs(f)5 b(;)17 b(g)t Fy(\))27
b(=)g Fs(g)t Fu(.)p Black 0 1206 a(Pr)-5 b(o)g(of.)p
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b Ft(\002)g Fs(B)5 b(;)17 b(p)1127 1221 y Fp(A)1183 1206
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b Fs(T)55 b Fy(b)s(e)42 b(an)g(ob)5 b(ject)42 b(in)g
Ft(C)48 b Fy(and)0 1323 y(let)40 b Fs(u)f Ft(2)h Fy(Mor)525
1338 y Fq(C)570 1323 y Fy(\()p Fs(T)8 b(;)17 b(A)27 b
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b Fy(:=)40 b Fs(p)1729 1338 y Fp(A)1813 1323 y Ft(\016)27
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y Ft(\016)27 b Fs(u)39 b Fy(:)g Fs(T)54 b Ft(\000)-60
b(!)39 b Fs(B)5 b Fy(.)65 b(Then)0 1439 y(\()p Fs(f)5
b(;)17 b(g)t Fy(\))27 b Ft(2)h Fy(Mor)521 1454 y Fq(C)566
1439 y Fy(\()p Fs(T)8 b(;)17 b(A)p Fy(\))h Ft(\002)g
Fy(Mor)1113 1454 y Fq(C)1158 1439 y Fy(\()p Fs(T)8 b(;)17
b(B)5 b Fy(\).)43 b(No)m(w)30 b(w)m(e)i(de\014ne)f Fs(h)p
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1454 y Fq(C)3636 1439 y Fy(\()p Fs(T)8 b(;)17 b(B)5 b
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1555 y Fy(\()p Fs(T)8 b(;)17 b(p)766 1570 y Fp(A)823
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y Fp(A)1249 1555 y Ft(\016)19 b Fs(u)27 b Fy(=)g Fs(f)39
b Fy(=)27 b Fs(p)1743 1571 y Fr(Mor)1871 1582 y Fl(C)1911
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b Fs(h)p Fy(\()p Fs(u)p Fy(\))31 b(and)g(Mor)2760 1570
y Fq(C)2805 1555 y Fy(\()p Fs(T)8 b(;)17 b(p)3001 1570
y Fp(B)3061 1555 y Fy(\)\()p Fs(u)p Fy(\))27 b(=)h Fs(p)3411
1570 y Fp(B)3491 1555 y Ft(\016)18 b Fs(u)28 b Fy(=)f
Fs(g)k Fy(=)0 1671 y Fs(p)49 1687 y Fr(Mor)176 1698 y
Fl(C)217 1687 y Fr(\()p Fp(T)6 b(;B)s Fr(\))421 1671
y Ft(\016)22 b Fs(h)p Fy(\()p Fs(u)p Fy(\).)0 1788 y(It)33
b(remains)g(to)g(sho)m(w)g(that)g Fs(h)f Fy(is)h(bijectiv)m(e.)46
b(W)-8 b(e)33 b(construct)g(the)g(in)m(v)m(erse)i(map)e(as)531
1951 y Fs(k)e Fy(:)d(Mor)844 1966 y Fq(C)889 1951 y Fy(\()p
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1966 y Fq(C)1490 1951 y Fy(\()p Fs(T)8 b(;)17 b(B)5 b
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end
%%Page: 65 65
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end
%%Page: 66 66
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%%Page: 69 69
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%%Page: 70 70
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%%Page: 79 79
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end
%%Page: 80 80
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%%Page: 81 81
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Fs(;)g(G)p Fy(-)o(\))2194 2577 y Ft(\030)2195 2609 y
Fy(=)2299 2605 y(Mor)2475 2620 y Fq(D)2536 2605 y Fy(\()p
Fs(F)2651 2564 y Fq(0)2674 2605 y Fy(-)o Fs(;)g Fy(-)o(\))p
Fs(:)0 2914 y Fy(By)33 b(the)g(Y)-8 b(oneda)33 b(Lemma)g(and)g(Prop)s
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2919 y Fy(=)2528 2914 y Fs(F)2605 2878 y Fq(0)2628 2914
y Fy(.)1168 b Fg(\003)p Black 0 3176 a Fy(3.1.3.)38 b
Fv(Corollary)-9 b(.)p Black 45 w Fu(L)k(et)40 b Fs(F)1029
3191 y Fp(i)1095 3176 y Fy(:)e Ft(C)43 b(\000)-57 b(!)37
b(D)43 b Fu(b)-5 b(e)40 b(left)g(adjoint)g(to)g Fs(G)2365
3191 y Fp(i)2431 3176 y Fy(:)e Ft(D)i(\000)-57 b(!)37
b(C)46 b Fu(for)40 b Fs(i)e Fy(=)f(1)p Fs(;)17 b Fy(2)p
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y Fr(1)0 3292 y Ft(\000)-57 b(!)38 b Fs(G)235 3307 y
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b(tr)-5 b(ansformation.)61 b(Then)40 b(ther)-5 b(e)40
b(is)h(a)f(unique)h(natur)-5 b(al)40 b(tr)-5 b(ansformation)40
b Fs(\014)k Fy(:)38 b Fs(F)3860 3307 y Fr(2)0 3408 y
Ft(\000)-57 b(!)27 b Fs(F)210 3423 y Fr(1)285 3408 y
Fu(such)34 b(that)i(the)e(diagr)-5 b(am)1108 3773 y Fy(Mor)1284
3788 y Fq(D)1344 3773 y Fy(\()p Fs(F)1445 3788 y Fr(1)1485
3773 y Fu(-)p Fs(;)17 b Fu(-)o Fy(\))651 b(Mor)2463 3788
y Fq(C)2508 3773 y Fy(\()p Fu(-)p Fs(;)17 b(G)2702 3788
y Fr(1)2741 3773 y Fu(-)p Fy(\))p 1665 3750 584 4 v 2166
3748 a Fo(-)1810 3704 y Fs(')1874 3719 y Fr(1)1914 3704
y Fy(\()p Fu(-)p Fs(;)g Fu(-)o Fy(\))1108 4163 y(Mor)1284
4178 y Fq(D)1344 4163 y Fy(\()p Fs(F)1445 4178 y Fr(2)1485
4163 y Fu(-)p Fs(;)g Fu(-)o Fy(\))651 b(Mor)2463 4178
y Fq(C)2508 4163 y Fy(\()p Fu(-)p Fs(;)17 b(G)2702 4178
y Fr(2)2741 4163 y Fu(-)p Fy(\))p 1665 4140 V 2166 4138
a Fo(-)1810 4232 y Fs(')1874 4247 y Fr(2)1914 4232 y
Fy(\()p Fu(-)p Fs(;)g Fu(-)o Fy(\))p 1370 4070 4 254
v 1372 4070 a Fo(?)846 3968 y Fy(Mor)1022 3983 y Fq(D)1083
3968 y Fy(\()p Fs(\014)6 b Fu(-)o Fs(;)17 b Fu(-)p Fy(\))p
2540 4070 V 2542 4070 a Fo(?)2581 3968 y Fy(Mor)2757
3983 y Fq(C)2802 3968 y Fy(\()p Fu(-)p Fs(;)g(\013)q
Fu(-)o Fy(\))p Black 0 4486 a Fu(Pr)-5 b(o)g(of.)p Black
41 w Fy(Giv)m(en)32 b Fs(A;)17 b(B)32 b Ft(2)c(D)s Fy(.)43
b(Then)32 b(there)f(is)g(a)g(unique)h(morphism)g Fs(\014)6
b Fy(\()p Fs(A)p Fy(\))27 b(:)h Fs(F)2846 4501 y Fr(2)2885
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(comm)m(utes)1127 4966 y(Mor)1303 4981 y Fq(D)1364 4966
y Fy(\()p Fs(F)1465 4981 y Fr(1)1504 4966 y Fs(A;)17
b Fy(-\))614 b(Mor)2482 4981 y Fq(C)2527 4966 y Fy(\()p
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1720 4943 549 4 v 2186 4941 a Fo(-)1830 4897 y Fs(')1894
4912 y Fr(1)1933 4897 y Fy(\()p Fs(A;)g Fy(-\))1127 5356
y(Mor)1303 5371 y Fq(D)1364 5356 y Fy(\()p Fs(F)1465
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y Fr(2)2799 5356 y Fy(-)o(\))p 1720 5334 V 2186 5332
a Fo(-)1830 5426 y Fs(')1894 5441 y Fr(2)1933 5426 y
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a Fo(?)772 5161 y Fy(Mor)948 5176 y Fq(D)1009 5161 y
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Fy(-)n(\))p 2578 5263 V 2579 5263 a Fo(?)2618 5161 y
Fy(Mor)2794 5176 y Fq(C)2839 5161 y Fy(\()p Fs(A;)g(\013)q
Fy(-)o(\))p Black Black eop end
%%Page: 85 85
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Fy(Mor)2700 1061 y Fq(C)2745 1046 y Fy(\()p Fs(B)5 b(;)17
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1148 a(?)873 1046 y Fy(Mor)1049 1061 y Fq(D)1110 1046
y Fy(\()p Fs(\014)6 b Fy(\()p Fs(A)p Fy(\))p Fs(;)17
b Fy(-)n(\))p 3069 1538 4 644 v 3070 1538 a Fo(?)3109
1241 y Fy(Mor)3285 1256 y Fq(C)3330 1241 y Fy(\()p Fs(A;)g(\013)q
Fy(-)o(\))1279 656 y(Mor)1455 671 y Fq(D)1516 656 y Fy(\()p
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560 y Fo(Q)1111 615 y(Q)1194 670 y(Q)1277 726 y(Q)1325
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656 y Fy(-)o(\))2588 560 y Fo(Q)2671 615 y(Q)2754 670
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1395 y(Q)1194 1450 y(Q)1277 1506 y(Q)1325 1538 y(Q)-83
b(s)2173 1436 y Fy(Mor)2349 1451 y Fq(C)2395 1436 y Fy(\()p
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1340 y Fo(Q)2671 1395 y(Q)2754 1450 y(Q)2837 1506 y(Q)2885
1538 y(Q)-83 b(s)3823 1873 y Fg(\003)0 2079 y Fy(There)30
b(is)f(an)f(equiv)-5 b(alen)m(t)31 b(de\014nition)e(of)f(adjoin)m(t)h
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b(First)28 b(w)m(e)i(need)0 2195 y(some)j(preparation.)p
Black 0 2388 a(3.1.4.)f Fv(Lemma.)p Black 44 w Fu(L)-5
b(et)35 b Fs(F)41 b Fy(:)28 b Ft(C)34 b(\000)-57 b(!)27
b(D)38 b Fu(and)c Fs(G)27 b Fy(:)h Ft(D)j(\000)-58 b(!)28
b(C)41 b Fu(b)-5 b(e)34 b(functors.)45 b(Then)34 b(the)h(map)641
2577 y Fy(Nat\(Id)928 2592 y Fq(C)974 2577 y Fs(;)17
b(GF)d Fy(\))27 b Ft(3)h Fy(\010)g Ft(7!)f Fs(G)p Fu(-)22
b Ft(\016)g Fy(\010)p Fu(-)28 b Ft(2)g Fy(Nat\(Mor)2363
2592 y Fq(D)2424 2577 y Fy(\()p Fs(F)14 b Fu(-)o Fs(;)j
Fu(-)p Fy(\))p Fs(;)g Fy(Mor)2909 2592 y Fq(C)2954 2577
y Fy(\()p Fu(-)p Fs(;)g(G)p Fu(-)p Fy(\)\))0 2766 y Fu(is)35
b(bije)-5 b(ctive)34 b(with)g(inverse)g(map)513 2955
y Fy(Nat)o(\(Mor)887 2970 y Fq(D)947 2955 y Fy(\()p Fs(F)14
b Fu(-)p Fs(;)j Fu(-)o Fy(\))p Fs(;)g Fy(Mor)1433 2970
y Fq(C)1478 2955 y Fy(\()p Fu(-)p Fs(;)g(G)p Fu(-)o Fy(\)\))28
b Ft(3)g Fs(')g Ft(7!)f Fs(')p Fy(\()p Fu(-)p Fs(;)17
b(F)d Fu(-)o Fy(\)\(1)2540 2970 y Fp(F)c Fu(-)2633 2955
y Fy(\))28 b Ft(2)g Fy(Nat\(Id)3080 2970 y Fq(C)3125
2955 y Fs(;)17 b(GF)d Fy(\))p Fs(:)0 3148 y Fy(Giv)m(en)34
b Fs(')28 b Fy(:)g(Mor)606 3163 y Fq(D)667 3148 y Fy(\()p
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b Fy(Mor)1277 3163 y Fq(C)1322 3148 y Fy(\(-)p Fs(;)17
b(G)p Fy(-)o(\))33 b(as)g(a)f(family)i Fs(')p Fy(\()p
Fs(C)r(;)17 b(D)s Fy(\))26 b(:)i(Mor)2715 3163 y Fq(D)2775
3148 y Fy(\()p Fs(F)14 b(C)r(;)j(D)s Fy(\))27 b Ft(\000)-60
b(!)28 b Fy(Mor)3476 3163 y Fq(C)3521 3148 y Fy(\()p
Fs(C)r(;)17 b(GD)s Fy(\).)0 3264 y(T)-8 b(ak)m(e)36 b
Fs(D)e Fy(:=)e Fs(F)14 b(C)7 b Fy(.)50 b(Then)35 b(w)m(e)h(get)f
(\010\()p Fs(C)7 b Fy(\))32 b(:=)f Fs(')p Fy(\()p Fs(C)r(;)17
b(F)d(C)7 b Fy(\)\(1)2172 3279 y Fp(F)j(C)2284 3264 y
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3900 y Fq(0)1847 3936 y Fy(\))p 3287 4038 V 3289 4038
a Fo(?)3328 3936 y Fs(')p Fy(\()p Fs(C)3507 3900 y Fq(0)3530
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b Ft(\016)g Fs(')p Fy(\()p Fs(C)2432 4410 y Fq(0)2455
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%%Page: 86 86
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