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MacLane S. — Categories for the working mathematician
MacLane S. — Categories for the working mathematician

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Название: Categories for the working mathematician

Автор: MacLane S.

Язык: en

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 263

Добавлена в каталог: 15.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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