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% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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readonly def
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currentdict end
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%%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
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readonly def
/FontBBox{-36 -250 1070 750}readonly def
currentdict end
currentfile eexec
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%%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
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dup 0 /minus put
dup 3 /asteriskmath put
dup 48 /prime put
dup 70 /F put
dup 71 /G put
readonly def
/FontBBox{-30 -955 1185 779}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 33 /omega put
dup 59 /comma put
dup 65 /A put
dup 66 /B put
dup 75 /K put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 118 /v 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 2 /multiply put
dup 33 /arrowright put
dup 35 /arrowdown put
dup 50 /element put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 80 /P put
dup 81 /Q put
readonly def
/FontBBox{-29 -960 1116 775}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 25 /germandbls put
dup 40 /parenleft put
dup 41 /parenright 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 53 /five put
dup 54 /six put
dup 58 /colon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 122 /z put
dup 127 /dieresis put
readonly def
/FontBBox{-34 -251 988 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%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 69 /E put
dup 75 /K put
dup 85 /U put
dup 97 /a put
dup 98 /b 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 110 /n put
dup 111 /o put
dup 114 /r put
dup 116 /t put
dup 117 /u put
dup 122 /z put
dup 127 /dieresis put
readonly def
/FontBBox{-33 -250 945 749}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 46 /period put
dup 48 /zero put
dup 50 /two put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 77 /M put
dup 80 /P put
dup 83 /S put
dup 85 /U put
dup 86 /V 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 127 /dieresis put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
currentdict end
currentfile eexec
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Ff(B)5 b Fh(\))27 b(:=)h Ff(f)1797 2322 y Fe(\000)p Fd(1)1891
2358 y Fh(\()p Ff(B)5 b Fh(\))31 b(f)2110 2362 y(\177)2107
2358 y(ur)g(jede)h(T)-8 b(eilmenge)33 b Ff(B)j Fh(v)m(on)c
Ff(Y)21 b Fh(.)32 b(Zeigen)315 2475 y(Sie,)h(da\031)f(damit)h
Fg(Q)28 b Fh(:)g Fj(Me)g Fg(\000)-60 b(!)28 b Fj(Me)33
b Fh(ein)g(k)m(on)m(tra)m(v)-5 b(arian)m(ter)34 b(F)-8
b(unktor)32 b(ist.)0 2649 y Fj(Aufgab)s(e)47 b(7.)e Fh(F)653
2653 y(\177)650 2649 y(ur)40 b(einen)h(V)-8 b(ektorraum)41
b Ff(V)61 b Fh(sei)41 b Ff(V)1936 2613 y Fe(\003)2016
2649 y Fh(=)f(Hom)2335 2664 y Fc(K)2403 2649 y Fh(\()p
Ff(V)5 b(;)17 b(K)7 b Fh(\))40 b(der)g(Dualraum)g(zu)g
Ff(V)22 b Fh(.)0 2765 y(F)67 2769 y(\177)64 2765 y(ur)37
b(einen)i(V)-8 b(ektorraumhomomorphism)m(us)40 b Ff(f)46
b Fh(:)36 b Ff(V)58 b Fg(\000)-60 b(!)36 b Ff(W)51 b
Fh(sei)38 b Ff(f)2516 2729 y Fe(\003)2591 2765 y Fh(:)e
Ff(W)2760 2729 y Fe(\003)2835 2765 y Fg(\000)-60 b(!)35
b Ff(V)3066 2729 y Fe(\003)3143 2765 y Fh(der)j(Homo-)0
2881 y(morphism)m(us)j(mit)d Ff(f)795 2845 y Fe(\003)835
2881 y Fh(\()p Ff(!)t Fh(\)\()p Ff(v)t Fh(\))e(:=)i Ff(!)t
Fh(\()p Ff(f)11 b Fh(\()p Ff(v)t Fh(\)\).)37 b(Zeigen)i(Sie,)g(da\031)f
(damit)h Fg(\000)2731 2845 y Fe(\003)2808 2881 y Fh(:)f
Fj(V)-9 b(ek)38 b Fg(\000)-60 b(!)37 b Fj(V)-9 b(ek)38
b Fh(ein)0 2998 y(k)m(on)m(tra)m(v)-5 b(arian)m(ter)34
b(F)-8 b(unktor)32 b(wird.)0 3172 y Fj(Aufgab)s(e)43
b(8.)g Fh(Seien)38 b Fg(F)43 b Fh(:)34 b Fg(C)40 b(\000)-59
b(!)33 b(E)45 b Fh(und)37 b Fg(G)j Fh(:)34 b Fg(D)i(\000)-59
b(!)33 b(E)45 b Fh(k)m(o)m(v)-5 b(arian)m(te)37 b(F)-8
b(unktoren.)37 b(Die)g(Komma-)0 3288 y(Kategorie)30 b(\()p
Fg(F)37 b(#)28 b(G)6 b Fh(\))30 b(ist)h(die)h(Kategorie)e(mit)h(T)-8
b(rip)s(eln)31 b(\()p Ff(A;)17 b(f)5 b(;)17 b(B)5 b Fh(\))30
b(als)h(Ob)5 b(jekten,)32 b(w)m(ob)s(ei)g Ff(A)c Fg(2)g(C)6
b Fh(,)0 3405 y Ff(B)53 b Fg(2)48 b(D)f Fh(und)e Ff(f)59
b Fh(:)48 b Fg(F)10 b Fh(\()p Ff(A)p Fh(\))47 b Fg(\000)-59
b(!)47 b(G)6 b Fh(\()p Ff(B)f Fh(\))45 b(in)f Fg(E)53
b Fh(sind.)46 b(Die)e(Morphismen)i(b)s(estehen)g(aus)f(P)m(aaren)0
3521 y(\()p Ff(g)t(;)17 b(h)p Fh(\))32 b(:)i(\()p Ff(A;)17
b(f)5 b(;)17 b(B)5 b Fh(\))33 b Fg(\000)-59 b(!)33 b
Fh(\()p Ff(A)984 3485 y Fe(0)1007 3521 y Ff(;)17 b(f)1110
3485 y Fe(0)1133 3521 y Ff(;)g(B)1256 3485 y Fe(0)1279
3521 y Fh(\))36 b(mit)g(\()p Ff(g)g Fh(:)e Ff(A)g Fg(\000)-60
b(!)33 b Ff(A)2047 3485 y Fe(0)2070 3521 y Ff(;)17 b(h)34
b Fh(:)f Ff(B)39 b Fg(\000)-60 b(!)33 b Ff(B)2606 3485
y Fe(0)2630 3521 y Fh(\))i(in)i Fg(C)30 b(\002)25 b(D)s
Fh(,)36 b(so)g(da\031)g(das)0 3637 y(Diagramm)1484 3775
y Fg(F)10 b Fh(\()p Ff(A)p Fh(\))147 b Fg(F)10 b Fh(\()p
Ff(A)2055 3739 y Fe(0)2078 3775 y Fh(\))p 1743 3752 90
4 v 1750 3750 a Fb(-)1714 3714 y Fe(F)d Fd(\()p Fc(g)r
Fd(\))1489 4165 y Fg(G)f Fh(\()p Ff(B)f Fh(\))158 b Fg(G)6
b Fh(\()p Ff(B)2049 4129 y Fe(0)2073 4165 y Fh(\))p 1738
4142 102 4 v 1757 4140 a Fb(-)1718 4104 y Fe(G)t Fd(\()p
Fc(h)p Fd(\))p 1598 4072 4 254 v 1599 4072 a Fb(?)1519
3962 y Fc(f)p 1987 4072 V 1989 4072 a Fb(?)2028 3965
y Fc(f)2069 3941 y Fa(0)0 4288 y Fh(k)m(omm)m(utiert.)34
b(Zeigen)f(Sie,)h(da\031)e(dieses)i(eine)g(Kategorie)e(ist.)100
5128 y(Abgab)s(e)g(Dienstag,)h(den)g(16.5.2000)e(11:15)h(Uhr)h(in)g
(der)g(V)-8 b(orlesung)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF