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Pareigis B. — Categories and functors
Pareigis B. — Categories and functors

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Название: Categories and functors

Автор: Pareigis B.

Язык: en

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 268

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$T_1$-space      74
Abelian category      158 163 164
Abelian group      4
Abelian group, divisible      14 18 148 163
Abelian group, finite      156
Abelian group, ordered      244
Abelian group, torsionfree      74 156
Additive category      158 159
Additive functor      178 179 222
Adjoint functor      51 91
Adjoint functor theorem      105 110 113
Adjunction of unit      148
Affine algebraic group      155
Algebra      68 126 127 147 149
Algebra, alternative      147
Algebra, canonical      126
Algebra, commutative      33 148 156
Algebra, equationally defined      127
Algebra, exterior      148
Algebra, finitely generated      135 138
Algebra, free      68 130 135
Algebra, generalized      156
Algebra, homomorphism      126
Algebra, Jordan      147 149
Algebra, Lie      147 149
Algebra, nil      148
Algebra, nilpotent      148
Algebra, polynomial      149 156
Algebra, sub-      130 138
Algebra, surjective      142
Algebra, symmetric      148 156
Algebra, tensor      148 156
Algebra, universal      120
Algebraic category      126
Algebraic functor      137 139 145
Algebraic theory      120 121 136 145
Algebraic theory of groups      125 126 155
Algebraic theory, consistent      121 136
Alternative algebra      147
Alternative ring      147
Amalgamated product      83
Analytic group      155
Anticommutative ring      146
Antiisomorphism      19
Artinian category      21
Artinian object      21
Artinian power set      21
Artinian ring      217
Associative ring      4 146
Associativity      2
Automorphism      17
Axiom of Choice      18 20 200 254
Azumaya      190 193 202 208
Balanced category      18 38 112
Base ring extension      149
Beck      72
Bernays      2 247
Bifunctor      39
Bimodule      147
Bound variable      248
Cancellable morphism, left      14
Cancellable morphism, right      14
Canonical algebra      126
Cartesian square      82
Cartesian square, со-      83
Categorical statement, exact      237 240
Categorical statement, full exact      241
Category      1 2 48
Category diagram      24 89
Category of Abelian groups      4 8 9 18 21 22 24 25 28 33 38 49 74 88 112 116 129 145 163 239 240
Category of algebras      64 147
Category of commutative C-algebras      33
Category of finite groups      16
Category of groups      3 8 16 18 21 22 24 28 33 38 50 74 88 129 146
Category of monoids      55 56
Category of pointed sets      3 8 22 28 33 38 112 129
Category of pointed topological spaces      5 8 22 24 28 33 38 112
Category of pointed topological spaces modulo homotopy      5 155
Category of R-modules      4 8 18 28 33 38 56 88 129 147 164 203 204 210
Category of rings      4 8 9 15 17 21 22 24 28 33 38 49 56 115 129 146 155 156
Category of small categories      8
Category of topological spaces      5 8 15 21 22 24 28 33 38 49 74 85 88 112 114 115 155
Category of topological spaces modulo homotopy      5
Category with (epimorphic) images      35
Category with (finite) coproducts      33
Category with (finite) intersections      34 170
Category with (finite) products      31
Category with (finite) unions      34 170
Category with (monomorphic) coimages      35
Category with colimits      78
Category with difference cokernels      28
Category with difference kernels      27
Category with zero morphisms      23
Category, abelian      158 163 164
Category, additive      158 159
Category, algebraic      126
Category, artinian      21
Category, balanced      18 38 112
Category, cocomplete      78 80
Category, complete      78 85
Category, coreflexive sub-      74
Category, directed      88
Category, directly connected      58
Category, discrete      6 81
Category, dual      12 19
Category, empty      3
Category, equivalent      18 55
Category, filtered      87
Category, finitely cocomplete      78 90
Category, finitely complete      78 85 89
Category, functor-      10 221
Category, Grothendieck      181 182 188
Category, hausdorff topological spaces      15 49 74 88 115
Category, inversely connected      60
Category, isomorphic      18
Category, large diagram      79
Category, locally cosmall      22
Category, locally noetherian      206
Category, locally small      21 112
Category, morphism      25
Category, noetherian      21
Category, of sets      3 8 13 14 17 18 20 21 22 23 26 28 32 33 38 49 50 55 85 88 99 101 112 129 156
Category, pointed      23
Category, product      39
Category, reflexive, sub-      73 114
Category, small      6 8 10 24
Category, sub-      9
Category, universally directly connected      59
Category, with limits      78
Center      215 216
Chain      21 255
Chain of subobjects      21 181
Chain, maximal condition      21
Chain, minimal condition      21
class      2 247
Class power      21
Class, special      247
Class, universal      251
Class, variable      247
Coarsest topology      112
Coirreducible object      208
Commutative algebra      33 148 156
Commutative diagram      9 24
Commutative group      4 155
Commutative polynomial algebra      149
Commutative ring      74 115 146
Commutativity condition      237
Commutator factor group      148
Compact Hausdorff space      74 114
Compact module      245
Compact module, со-      245
Compact object      204
Compactification, Stone — Cech      114
Complement      249
Complete category      78 85
Complete category, finitely      78 85 89
Complete category, со-      78 90
COMPLEX      167
composition      2
Composition series      174
Composition series, factor of      174
Composition series, length of      174
Condition commutativity      237
Condition exactness      237
Condition, Grothendieck      181
Congruence      141
Connected category, directly      58
Connected category, inversely      60
Connected category, universally directly      59
Connected category, universally inversely      60
Connecting homomorphism      243
Connection      58
Consistent algebraic theory      121 136
Constant functor      77 79
Construction      see Standard construction
Continuous functor      86
Continuous functor, со-      86
Continuous map      5
Continuous map, dense      15
Continuous map, pointed      5
Contra variant functor      7
Contractible pair      69
Correspondence of sets      6
Counterimage      34 35 97
Covariant functor      7
Creation of difference cokernels      70
Creation of isomorphisms      69
Creation properties      69
Cube lemma      15
Decomposable object      190
Decomposable object, in-      190
Decomposition, Q-S-      118
Dense continuous map      15
Derived functor, zeroth right-      233
Diagonal      33 159
Diagonal, со-      33 159
Diagram      9 24
Diagram, category      24 89
Diagram, commutative      9 24
Diagram, empty      86
Diagram, large      79
Diagram, large diagram category      79
Diagram, scheme      6 24 237
Difference cokemel      26 28 70 81 163
Difference cokemel, kernel      26 81—86 163
Difference cokemel, quotient object      28
Difference cokemel, subobject      28
Direct limit      81 88
Direct limit, exact      185
Direct sum      159
Directed category      88
Directed family of subobjects      182
Directly connected category      58
Directly connected category, universally      59
Discrete category      6 81
Discrete topological space      8 112
Divisible abelian group      14 18 148 163
Domain      3 250
Double dual space      12
Dual category      12 19
Dual standard construction      62
Dual theorem      13
Duality      12
Duality, principle      13
Ehrbar      118
Eilenberg      62 256
Element, nilpotent      192
Embedding theorem      236
Empty category      3
Empty diagram      86
Empty product      31
Empty set      251
Endofunctor      62
Endomorphism      17
Endomorphism of identity functor      216
Endomorphism ring      163
Epimorphic image      34
Epimorphism      14
Epimorphism, relative      118
Epimorphism, relatively split      141
Equationally defined algebra      127
EQUIVALENCE      18 55
Equivalence relation      6 99
Equivalence relation, monomorphic      99
Equivalence relation, pre-      101
Equivalent category      18 33
Equivalent monomorphism      20
Essential extension      197 198
Essential extension, largest      198
Essential extension, maximal      198
Evaluation functor      43 45 46
Evaluation map      11
Exact categorical statement      237 240
Exact categorical statement, full      241 242
Exact direct limit      185
Exact functor      179
Exact sequence      166
Exact sequence, exactness condition      237
Exact sequence, short      166
Exchange theorem      209 245
Extension, base ring      149
Extension, essential      197 198
Extension, injective      198
Extension, largest essential      198
Extension, maximal essential      198
Extension, minimal injective      198
Extension, smalles injective      198
Exterior algebra      148
Factor of composition series      174
Faithful functor      44 115 116
Family      253
Fiber product      82—84 168
Fiber product, со-      83 85 169
Fiber sum      83
Field      148
Field, skew-      219
Filtered category      87
Filtered colimit      88
Filtered limit      88
Final object      22 84 86
Finite poduct      84
Finite projective object      210
Finitely cocomplete category      78 90
Finitely complete category      78 85 89
Finitely generated algebra      135 138
Finitely generated module      205
Finitely generated object      204
Forgetful functor      8 129
Formula      248
Free algebra      68 130 135
Free algebraic theory      123
Free object, relatively      141
Free variable      248
Full exact categorical statement      241 242
Full faithful functor      115 117
Full functor      44 115 116
Full matrix ring      219
functor      6 7
Functor, additive      178 179 222
Functor, adjoint      51 91
1 2 3
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