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| Авторизация |
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| MacLane S. — Categories for the working mathematician |
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| Предметный указатель |
Ab-category 17 24 29 190 194
Abelian categories 194 ff.
Abelian groups 24
Absolute coequalizer 145
Absolute Kan extension 245
Absolute limit 145
Action group 137
Action of operators 120
Addition of arrows 192
Addition, ordinal 171
Additive, category 192
Additive, functor 28 83 193 238
Additive, Kan extension 238
Adjoint 2 85
Adjoint, equivalence 91
Adjoint, functor 38 79
Adjoint, pairs 93
Adjoint, square 101 ex.
Adjointness 2
Adjunct 79
Adjunction 78 80 81
Adjunction with a parameter 100
Algebraic system 120
Algebras, morphisms of T 136
Amalgamated product 66
Arity 120
Arrows, addition of 194 ex.
Arrows, canonical 74 101 165
Arrows, function 13
Arrows, only-metacategory 9
Associative law 8
Associative law for monad 134
Associative law for monoid 159
Associative law for monoidal categories 162
Associative law for T-algebra 136
Associative law, general 167 168 171
Associativity 7
Atomic statement 31
Augmentation 46 175
Augmented simplicial object 175
Barycentric coordinates 174
Base point 26 184
Based category 180
Basic arrows 162
Basic graphs 162
Beck’s theorem 147
Bifunctor 37 191 210
Bilinear composition 28
Binary relation 26
Binary words 161
Biproduct 190 ff.
Bound variable 31 219
Bound, greatest lower 110 122
Bound, least upper 110 122
Boundary homomorphism 175
Boundary of tetrahedron 174
Cancellable (left or right) 19
Canonical arrow 74 110 167 189 21
Canonical map 165 167
Canonical presentation 149
Cartesian, closed category 95
Cartesian, product 2 21
Cartesian, square 71
Category 7 10 27
Category of adjunction 99
Category of arrows 40
Category, Ab 28
Category, abelian 194
Category, additive 192
Category, based 180
Category, cartesian closed 95
Category, closed 180
Category, co-well powered 126
Category, comma 47
Category, complete 105 106
Category, concrete 26
Category, connected 86
Category, discrete 11
Category, double 44
Category, dual 33
Category, empty 229
Category, enriched 181
Category, equivalence of 20 91
Category, fibered 35
Category, filtered 207
Category, free 50
Category, functor 40 44 115
Category, image 243 ex.
Category, isomorphism of 90
Category, large 12 23
Category, locally small 127
Category, monoidal 157 158 167 176
Category, monoidal, free 166 ex.
Category, monoidal, strict 157 160 171
Category, monoidal, symmetric 180
Category, opposite 33
Category, preadditive 28
Category, product 36
Category, pseudo-filtered 212
Category, relative 180
Category, simplicial 12 171
Category, subdivision 220
Category, super-comma 111 ex.
Category, two-dimensional 44 102
Category, well-powered 126
Category, well-powered of adjunctions 99
Category, well-powered of algebras 124
Category, well-powered of arrows 40
Category, well-powered of diagrams 53
Category, well-powered of small sets 12 24
Chain complex 177 198
Character group 17
Chase, diagram 75 200
class 23
Class, equational 120
Closed category 180
Closed, cartesian — categories 95
Closure operation 135 137 153
Co-well-powered category 126
Cochain complex 179
Cocomponents of a map 74
Codense functor 242
Codensity monad 246
Codomain 7 10
Coend 222 236
Coequalizers 64
Coequalizers, absolute 145
Coequalizers, creation of 147 152
Coequalizers, split 146
Cogenerating set 123
Cogenerator 123
Coherence theorem 157 161
Coimage 196
Cokernel 64
Cokernel pair 66
Colimit 67 208 210 229 236
Colimit, filtered 208
Colimit, reflection of 150
Comma category 47
Commutative diagram 1 8
Commutator 17
Commutator, subgroup 14
Comonad 135 177
Compact Hausdorff space 153
Compact-open topology 181
Compactification 121 127
Compactly generated spaces 181
Comparison, functor 139 150 152
Comparison, theorem 144
Complete category 105
| Component 69 214
Component, connected 88 ex.
Component, matrix of 192
Component, matrix of natural transformation 16
Component, matrix of wedge 219
Composable pair 9 10 13 49
Composable pair of arrows 9 10 49 196
Composite 7 14
Composite, horizontal 42 102 133
Composite, vertical 42 99 102
Composite, vertical function 9
Composite, vertical functor 14 43
Composite, vertical of paths 20
Composite, vertical of transformations 40 102
composition 7 27
Comprehension principle 21
Concrete category 26
Cone 67 71 106
Cone, canonical 242
Cone, colimiting 67 210
Cone, limiting 67 69 211
Cone, universal 67
Congruence 52
Conjugate natural transformation 99 102
Conjugation 18 ex. 20
Connected, category 86
Connected, component 88 ex.
Connected, groupoid 20
Connected, sequence of functors 238
Connecting arrows 203
Connecting homoraorphism 202 238
Connection, Galois 93 94
Continuous functor 112
Continuous map 153 181
Contractible parallel pair 146 ex.
Contravariant functor 17 33
Contravariant hom-functor 34
Coordinates, barycentric 174
Copowers 64 237
Coproduct 62
Coproduct, denumerable 168
Coproduct, finite 208
Coproduct, infinite 64 208
Coproduct, injections of 63
Coproduct, injections of diagram 62
Coproduct, injections of object 63
Coreflective 89 181
Counit of adjunction 81 85
Covariant, functor 34
Covariant, hom-functor 34
Covariant, power-set functor 138 ex.
Creation of coequalizers 147 152
Creation of ends 221
Creation of limits 108
CTT-Crude tripleability theorem 151 ex.
Degeneracy 175
Dense, functor 242
Dense, subcategory 241
Derived, functor 238
Derived, operator 120
Determinent 16
Diagonal arrow 84 189
Diagonal arrows 84 ex. 189
Diagonal functor 67
Diagonal map 73 192
Diagram 2 3 4 51 71 196
Diagram, biproduct 190
Diagram, category of 53
Diagram, commutative 3 8 161
Diagram, coproduct 62
Diagram, limit 69 71
Diagram, product 69
Diagram, product, chase 75 200
Diagram, product, scheme 10 49 51
Difference kernel 70
Difference member 204
Dinatural transformation 214
Direct product 69
Direct sum 191
Directed preorder 207
Directed set 207
Disjoint, hom-sets 27
Disjoint, union 63
Domain 7 10
Double category 44
Double end 226
Dual 31
Dual category 33
Duality principle 32
Dummy 215
Eilenberg — Moore category of a monad 135
Element, universal 57
Embedding 15
Empty category 10 229
Empty functor 229
END 218
End, creation of 221
End, double 226
End, interchange of 237
End, preservation of 221
End, preservation of natural transformation 224
Ending wedge 219
Endofunctor 133
Enriched category 181
Epi 19
Epi arrows 19 190
Epi, split 20
Epi, split, monic factorization 190 195
Equalizer 70 109 129
Equational class 120
Equivalence, adjoint 91
Equivalence, natural 16
Equivalence, natural of categories 18 91
ETAC 31
Euclidean vector spaces 216
Evaluation map 96 216
Exact 196
Exact, left functor 197
Exact, right sequence 197
Exact, short sequence 196
Exact, short sequence, functor 197
Extensions 229
Extensions, absolute Kan 245
Extensions, Kan 229
Extensions, Kan, left 238
Extensions, Kan, right 232 233
Extranatural transformation 215
Face operator 175
Factorization of arrows 195
Faithful functor 15
Fiber map 71
Fibered category 35
Fibered product 71
Fibered sum 66
Fields of quotients 56
Filtered category 207
Filtered coiimit 208
Filtered set 207
Final functor 213 234
Final subcategory 213
Finite limit 109
Finite product 72
Five lemma 198 201
Forgetful functor 14 85 116 140 153 170 208
Fork, split 145
Formal criteria for a universal arrow 231
Formal criteria for existence of adjoint 230 244
Formal criteria for representability 231
Free category 50
Free monoid 51
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