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%%BeginFont: CMSY10
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%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
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/FullName (CMSY10) readonly def
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/Weight (Medium) readonly def
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readonly def
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currentdict end
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%%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 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}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 26 /rho put
dup 32 /psi put
dup 39 /phi1 put
dup 59 /comma put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 88 /X put
dup 89 /Y put
dup 102 /f put
dup 105 /i put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-30 -250 1026 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 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 51 /three put
dup 53 /five put
dup 58 /colon put
dup 61 /equal put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 77 /M put
dup 79 /O 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 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 120 /x 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 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 73 /I put
dup 77 /M put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 85 /U 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 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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50 29[84 59 72 1[77 52 7[50 4[0 3[66 8[100 7[100 29[50
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rf /Fd 134[48 55 14[33 2[48 12[57 81 20[70 74 73 3[49
1[27 19[64 6[63 5[50 26[{}14 99.6264 /CMMI12 rf /Fe 128[49
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rf /Fg 128[56 8[59 62 44 44 46 2[56 62 93 31 2[31 62
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TeXDict begin 1 0 bop 115 355 a Fg(Mathematisc)m(hes)39
b(Institut)100 471 y(der)33 b(Univ)m(ersit)742 476 y(\177)743
471 y(at)h(M)984 476 y(\177)981 471 y(unc)m(hen)206 588
y(Prof.)j(Dr.)g(B.)g(P)m(areigis)3104 354 y(SS)h(2000)3124
471 y(Blatt)f(4)413 1084 y Ff(\177)396 1116 y(Ubungen)45
b(zu)f(Einf)1374 1121 y(\177)1370 1116 y(uhrung)g(in)g(die)f
(Kategorien)l(theorie)0 1370 y Fg(Aufgab)s(e)53 b(13.)48
b Fe(Zeigen)d(Sie,)h(da\031)f(die)g(Kategorie)g(der)g(Ringe)h(\(mit)f
(Einselemen)m(t\))j Fg(Ri)c Fe(k)m(ei-)0 1487 y(nen)50
b(Kogenerator)g(b)s(esitzt.)h(\(Hin)m(w)m(eis:)h(Zeigen)e(Sie)h(f)2116
1491 y(\177)2113 1487 y(ur)e(einen)i(Kogenerator)f Fd(C)56
b Fe(zun)3379 1491 y(\177)3379 1487 y(ac)m(hst)0 1603
y Fg(R)p Fd(i)p Fe(\()p Fc(Z)p Fd(=)p Fe(2)p Fc(Z)p Fd(;)17
b(C)7 b Fe(\))46 b Fb(6)p Fe(=)g Fb(;)d Fe(und)h Fg(R)p
Fd(i)p Fe(\()p Fc(Z)p Fd(=)p Fe(3)p Fc(Z)p Fd(;)17 b(C)7
b Fe(\))46 b Fb(6)p Fe(=)g Fb(;)d Fe(und)h(leiten)g(Sie)g(daraus)g
(einen)h(Widerspruc)m(h)0 1719 y(her.\))0 2012 y Fg(Aufgab)s(e)57
b(14.)50 b Fe(Seien)g Fb(F)10 b Fd(;)17 b Fb(G)61 b Fe(:)55
b Fb(C)62 b(!)55 b(D)c Fe(F)-8 b(unktoren)49 b(und)h
Fd(')55 b Fe(:)g Fb(F)65 b(!)55 b(G)g Fe(eine)50 b(nat)3319
2016 y(\177)3316 2012 y(urlic)m(he)0 2128 y(T)-8 b(ransformation.)39
b(Zeigen)h(Sie:)g Fd(')f Fe(ist)g(ein)h(nat)1782 2132
y(\177)1779 2128 y(urlic)m(her)g(Isomorphism)m(us)i(genau)d(dann,)h(w)m
(enn)0 2244 y(alle)33 b Fd(')p Fe(\()p Fd(X)8 b Fe(\))27
b(:)h Fb(F)10 b Fe(\()p Fd(X)e Fe(\))27 b Fb(!)g(G)6
b Fe(\()p Fd(X)i Fe(\))32 b(\(f)1224 2248 y(\177)1221
2244 y(ur)h(alle)g Fd(X)i Fb(2)28 b(C)6 b Fe(\))33 b(Isomorphismen)i
(in)d Fb(D)k Fe(sind.)0 2537 y Fg(Aufgab)s(e)47 b(15.)f
Fe(Charakterisieren)c(Sie)e(diejenigen)i(Morphismen)f
Fd(f)51 b Fe(:)41 b Fd(A)f Fb(!)g Fd(B)5 b Fe(,)40 b(f)3182
2541 y(\177)3179 2537 y(ur)g(die)g(die)0 2653 y(nat)144
2657 y(\177)141 2653 y(urlic)m(he)34 b(T)-8 b(ransformation)1263
2810 y Fb(C)6 b Fe(\()p Fd(f)f(;)17 b Fe(-\))27 b(:)h
Fb(C)6 b Fe(\()p Fd(B)f(;)17 b Fe(-\))27 b Fb(!)h(C)6
b Fe(\()p Fd(A;)17 b Fe(-)o(\))0 2967 y(ein)43 b(nat)311
2971 y(\177)308 2967 y(urlic)m(her)h(Monomorphism)m(us)h(ist.)f(\(Eine)
g(nat)2060 2971 y(\177)2057 2967 y(urlic)m(he)g(T)-8
b(ransformation)43 b Fd(')i Fe(:)g Fb(F)54 b(!)45 b(G)0
3083 y Fe(hei\031t)35 b(nat)390 3087 y(\177)387 3083
y(urlic)m(her)h(Monomorphism)m(us,)h(w)m(enn)f(f)1847
3087 y(\177)1844 3083 y(ur)e(alle)h(F)-8 b(unktoren)35
b Fb(H)h Fe(und)f(alle)f(nat)3264 3087 y(\177)3261 3083
y(urlic)m(hen)0 3199 y(T)-8 b(ransformationen)33 b Fd( )t(;)17
b(\032)28 b Fe(:)g Fb(H)h(!)e(F)42 b Fe(gilt)32 b Fd(' )g
Fe(=)27 b Fd('\032)h Fe(=)-17 b Fb(\))28 b Fd( )k Fe(=)27
b Fd(\032)p Fe(.\))0 3492 y Fg(Aufgab)s(e)51 b(16.)c
Fe(Sei)c Fb(F)55 b Fe(:)46 b Fb(C)51 b(!)46 b Fg(Me)d
Fe(der)g(k)m(o)m(v)-5 b(arian)m(te)45 b(F)-8 b(unktor)43
b(mit)g Fb(F)10 b Fe(\()p Fd(Y)21 b Fe(\))45 b(=)g Fb(f\003g)e
Fe(f)3322 3496 y(\177)3319 3492 y(ur)g(alle)0 3608 y
Fd(Y)61 b Fb(2)39 b(C)6 b Fe(.)40 b(Seien)g Fd(X)48 b
Fb(2)39 b(C)46 b Fe(ein)40 b(Ob)5 b(jekt)40 b(und)g Fd(x)1699
3623 y Fa(0)1778 3608 y Fb(2)g(F)10 b Fe(\()p Fd(X)e
Fe(\))38 b(so)i(gegeb)s(en,)g(da\031)f(f)2925 3612 y(\177)2922
3608 y(ur)g(jedes)i(Ob)5 b(jekt)0 3724 y Fd(Y)54 b Fb(2)33
b(C)41 b Fe(und)36 b(jedes)h(Elemen)m(t)g Fd(y)f Fb(2)d(F)10
b Fe(\()p Fd(Y)21 b Fe(\))35 b(genau)h(ein)g(Morphism)m(us)h
Fd(f)44 b Fe(:)32 b Fd(X)41 b Fb(!)32 b Fd(Y)57 b Fe(so)35
b(existiert,)0 3840 y(da\031)d Fb(F)10 b Fe(\()p Fd(f)h
Fe(\)\()p Fd(x)494 3855 y Fa(0)533 3840 y Fe(\))28 b(=)f
Fd(y)36 b Fe(gilt.)c(Zeigen)h(Sie,)h(da\031)e(dann)h
Fd(X)40 b Fe(ein)33 b(Anfangsob)5 b(jekt)34 b(in)f Fb(C)39
b Fe(ist.)100 5128 y(Abgab)s(e)32 b(Dienstag,)h(den)g(30.5.2000)e
(11:15)h(Uhr)h(in)g(der)g(V)-8 b(orlesung)p eop end
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userdict /end-hook known{end-hook}if
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