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| MacLane S. — Categories for the working mathematician |
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| Предметный указатель |
Free monoidal category 162
Free product 124 ex. 210
Free T-algebra 136
Freyd adjoint functor theorem 117
Freyd existence theorem for an initial object 116 231
Freyd’s adjoint functor theorem 117
Front and back adjunction 81
Full functor 14
Function 8
Function, arrow 13
Function, composite 9
Function, identity 9
Function, inclusion 9
Function, insertion 9
Function, monotone 172
Function, object 13
Function, order preserving 94
Function, order preserving set 40
functor 3 13
Functor, additive 29 83 193 238
Functor, adjoint 79
Functor, codense 242
Functor, comparison 138
Functor, composite 14
Functor, continuous 112
Functor, contravariant. 17 35
Functor, covariant 34 138
Functor, dense 242
Functor, derived 238
Functor, diagonal 67
Functor, empty 229
Functor, exact 197
Functor, faithful 15
Functor, final 213 234
Functor, forgetful 14 85 116 140 153 170 208
Functor, full 14
Functor, identity 14 165
Functor, inclusion 15
Functor, left adequate 246
Functor, left exact 197
Functor, morphism of 16
Functor, power-set 13 33
Functor, representable 61
Functor, underlying 14
Functor, Yoneda 61
Functor, Yoneda category 40
Fundamental groupoid 20
Galois connections 93 ff.
General linear group 14
Generating object 123
Generating set 121
Generators of a category 52
Geometric realization 223
Godel — Bernays axioms 23
Graded set 120
Graph 10 48
Group 11 20 75
Group, fundamental 20
Group, small 22
Group, small in a category 3
Group, small, actions 137
Groupoid 20
Hausdorff spaces 121 131
Hausdorff spaces, compact 121 153
Hausdorff spaces, compactly generated 181
Hom-functor 35 193
Hom-functor, contravariant 34
Hom-functor, covariant 34
Hom-sets 10 27 180
Hom-sets, disjoint 27
Homology 175 198
Homology, singular 175
Homomorphism see “Morphism”
Homomorphism, boundary 175
Homomorphism, connecting 202
Homomorphism, crossed 179 (see also “Morphism”)
Homotopy class of maps 12 13 25
Homotopy class of paths 20
Horizontal composite 42 102 133
Horn-object 180
Idempotent 20
Idempotent arrows 20
Idempotent, split 20
Identities for algebras 120
Identity 7 (see also “Unit”)
Identity arrows 7 8 12 190
Identity, triangular 83
Identity, triangular, arrow 7 8 10
Identity, triangular, function 9
Identity, triangular, functor 14 43 165
Identity, triangular, natural transformation 43 ff.
Image 196
Inclusion, function 9
Inclusion, functor 15
Induced map 34
Infinite coproduct 64
Infinite product 69
Initial functor 214
Initial object 20 229
Initial object, existence of 116 231
Injection 15 19
Injection of coproduct 63
Injective, monotone function 172
Injective, object 114
Insertion function 9
integral 219
Integral, double 226
Integral, iterated 226
Interchange of ends (Fubini) 237
Interchange, law 44 134
Internal horn functor 180
Intersection of subobjects 122
Intertwining operator 41
Inverse 14
Inverse, left adjoint-left 92
Inverse, left or right 19
Inverse, two-sided 14
Inverse, two-sided, limit 68
Invertible arrow 19
Invertible arrows 19
Isomorphism 14
Isomorphism, natural 16
Isomorphism, reflection of 150
Isomorphism, reflection of categories 14 90
Isomorphism, reflection of objects 19
Iterated integral 226
Join 110 122
Kan extensions 229 ff.
Kan extensions, absolute 245
Kan extensions, additive 238
Kan extensions, left, as coends 238
Kan extensions, pointwise 240
Kan extensions, right 232 ff. 240
Kelley spaces 181
Kelleyfication 182 ff.
Kernel 187
Kernel of arrows 187
Kernel, difference 70
Kernel, difference pair 71
Kleisli category of a monad 143
Large category 23
Least upper bound 63
Left action 170
Left action of a monoid 170
Left adequate functor 246
Left adjoint 2 38 70 85 230
Left adjoint left-inverse 92
Left adjoint, inverse 92
Left adjoint-right-inverse 130
Left cancellable 19
| Left exact functor 197
Left inverse 19
Left Kan extensions 238 244
Left regular representation 170
Lemma, five 201
Lemma, short five 198
Lemma, snake 202
Lemma, Yoneda 61
Length of words 161
LIMIT 68 76.109 211 229 234
Limit, creation of 108
Limit, direct 67
Limit, filtered 212
Limit, finite 109 211
Limit, inductive 67
Limit, inverse 68
Limit, pointwise 112 233
Limit, preservation of 112
Limit, projective 68
Limit, projective of a natural transformation 224
Limit, projective, object 68
Limiting cone 67 68 114 232
Linear order 11
Locally small category 127
Loop space 185
MAP see “Arrow”
Map of adjunction 97
Map, canonical 165 211 242
Map, continuous 13 153 181
Map, diagonal 73 192
Map, evaluation 96
Map, fiber 71
Map, homotopic 13
Map, structure, of adjunctions 97
Map, structure, of algebras 136 139 148
Matrices 11 74 192
Matrix multiplication 74 192
Meet 110 122
Member 200
Metacategory 7 ff.
Metagraph 7
Modules 12 28 138
Monad 133 135 176
Monad defined by adjunction 135
Monad, Codensity 246 ex.
Monad, free group 135
Monad, multiplication of 134
Monad, unit of 134
Monad, unit of denned by adjunction 135
Monadic 139
Monic arrows 19 190
Monic, split 20
Monic, split, arrow 19
Monoid 2 4 11 75 134 166
Monoid, free 51 168
Monoid, universal 157
Monoidal categories 4 157 158 165
Monoidal categories, free 168
Monoidal categories, strict 157 171
Monoidal categories, symmetric 180
Monotone function 15 ex. 172
Morphisms 9
Morphisms of arrows 9
Morphisms of categories 13
Morphisms of functors 16
Morphisms of graphs 48
Morphisms of monoidal categories 162
Morphisms of monoidal categories, relaxed 160
Morphisms of monoidal categories, strict 160
Morphisms of short exact sequences 198
Morphisms of simplicial objects 174
Morphisms of T-algebras 136
Multiplication in a monad 134
Multiplication of monoidal categories 158 161
Natural 38 217 234
Natural components of — transformation 16
Natural conjugate — transformation 98
Natural universal transformation 39
Natural universal transformation, bijection 2
Natural universal transformation, equivalence 16
Natural universal transformation, isomorphism 16 216
Natural universal transformation, transformation 16 97
Null object 20 187 190 196
Number, ordinal 11 171
O-graph 49
Object 7 10 48 180
Object, coproduct 63
Object, free 143
Object, homology 198
Object, initial 20 229
Object, injective 114
Object, limit 68
Object, null 20 187 190
Object, projective 114
Object, quotient 122
Object, simplicial 174 175
Object, terminal 20 73
Object, terminal, function 13
Object, terminal, over 46
Object, terminal, under 46
Operator 120
Operator, derived 120
Operator, intertwining 41
Order, linear 11
Order, partial 11
Order, partial, preserving function 93 ff.
Ordinal, finite 12 171 176
Ordinal, finite, addition 171
Ordinal, finite, number 11
p-adic, integers 107
P-adic, solenoid 107
Pair, adjoint 93
Pair, cokernel 66
Pair, composable 9 49 196
Pair, conjugate 102
Pair, equalizer of 70 109
Pair, kernel 71
Pair, parallel 11 65 70
PARAMETER 99 111 216
Parameter, adjunction with a 100 216
Parameter, adjunction with, theorem 224 225
Partial order 11
Path 50
Path, directed 163
Pointed set 26
Pointed topological space 26 184
Pointwise, Kan extensions 239 ff.
Pointwise, limit 112
Power 70
Power set 21
Power set functor 13 33
Preadditive category 28
Precategory 49
Precise tripleability theorem (Beck) 150
Preorder 11 93
Preorder, directed 207
Presentation, canonical 149
Preservation end of functor 221
Preservation of coproduct 168
Preservation, limit 112
Preservation, right Kan extension 239—240
PRODUCT 1 69
Product, amalgamated 66
Product, cartesian 2
Product, direct 69
Product, fibered 71
Product, free 124 ex. 210
Product, infinite 69
Product, iterated 172 176
Product, projections of 1 36 69
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