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| Pareigis B. — Categories and functors |
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| Предметный указатель |
 -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
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