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| Авторизация |
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| Поиск по указателям |
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| Borceux F. — Handbook of Categorical Algebra, Volume 1: Basic Category Theory |
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| Предметный указатель |
 -filtered category 268
-filtered colimit 268
-flat functor 270
-left-exact functor 269
-limit 268
2-category 282
3-category 292
Absolute colimit 66
Absolutely flat functor 271
Adjoint arrows 284 305
Adjoint functor theorem 109
Adjoint functors 98
Adjunction 98
arrow 4
Associativity of coproduct 45
Associativity of pullback 54
Axiom of universes 3
Bicategory 302
Bidense morphism 235
Bifunctor 23
Bilimit 295
Bimodule 307 308
Calculus of fractions 183
Cartesian closed category 335
Category 4
Category of arrows over I 7
Category of arrows under I 7
Category of elements 22
Category of fractions 181
Category with absolute colimits 272
Category with enough projectives 164
Category, n-category 293
Cauchy complete category 274
Cauchy completeness 319
Cauchy completion 277
cell 283
Cell, 0-cell 283
Cell, 1-cell 283
Cell, 2-cell 283
Cell, 3-cell 292
class 3
Closed subobject 228
Closure of a subobject 227
CoCone 57
Codomain of an arrow 5
Coequalizer 49
Cogenerator 167
Colimit 57
Colimit closed class 205
Collectively faithful family of functors 154
Comma category 20 91
Commutative diagram 5
Commutativity condition 177
Complete category 59 107
Conditional graph 178
Cone 56
Cone, lax cone 300
Cone, pseudo-cone 300
Connected category 58
Constant natural transformation 15
Contravariant functor 16
Coproduct 44
Coreflection along a functor 98
Covariant functor 16
Crossed module 339
Dense family of generators 153
Dense generator 153
Dense subobject 228
Discrete category 7
distributor 308
Domain of an arrow 5
Dual category 33
Duality principle 33
Epimorphism 27
Epireflective subcategory 120
Equalizer 48
EQUIVALENCE 284
Equivalence of categories 116
Essential localization of a category 119
Extremal epimorphism 136
Factorization 148
Factorization system 209
Faithful functor 19
Family of functors collectively reflecting isomorphisms 154
Family of generators 151
Filtered category 76
Filtered colimit 76
Final functor 69
Final object 48
Finitely complete category 59
Finitely generated category 63
Finitely well-complete category 147
Flat functor 260
Forgetful functor 8
Free Abelian group 102
Free group 102
Free monoid 102
Free ring 103
Full and faithful functor 19
Full functor 19
Full subcategory 19
functor 5
Functor 2-functor 287
Functor horn-functor 34
Functor lax functor 296
Functor preserving monomorphisms 24
Functor pseudo-functor 297
Functor reflecting monomorphisms 24
Galois connection 105
| Generator 151
Godement product of natural transformations 13
Graph 176
Groupoid 287
Homotopy 285
Idempotent 271
Identity arrow 4
Identity functor 6
Initial object 48
Injective object 167
Internal 325
Internal automorphism 287
Internal base-valued functor 329
Internal category 325
Internal category of elements 331
Internal colimit 333
Internal constant functor 328 330
Internal distributor 339
Internal dual category 328
Internal filtered category 331
Internal flat functor 333
Internal functor 327
Internal limit 333
Internal natural transformation 327 329
Internal power 335
Internal presheaf 329
Internal product 335
Intersection 133
Isomorphism 19 31
Kan extension 113 284
Kernel pair 52
Left adjoint functor 98
Left exact functor 250
Lepi-strong-mono factorization 149
LIMIT 56
Limit preserving functor 64
Limit reflecting functor 65
Limit, 2-limit 293
Limit, bilimit 395
Limit, lax-limit 300
Limit, pseudo-limit 300
Localization of a category 119
Locally Cartesian closed category 339
Locally presentable category 241
Loop 104
Modification 290 298
Monomorphism 23
More general adjoint functor theorem 277
Morita equivalent categories 321
Morphism 4
Morphism of graphs 176
Natural transformation 10 16
Natural transformation, 2-natural transformation 289
Natural transformation, lax-natural transformation 297
Natural transformation, pseudo-natural transformation 298
Object 4
Orthogonal subcategory 197
Orthogonality 193 194
Path 176
Path category 177
Pointwise Kan extension 124
Presentable object 297
PRODUCT 39 40
Product of categories 22
Product, associativity of 40 41
Profunctor 308
Projective object 163
Pullback 51
Pushout 52
Quotient 132
Reflection along a functor 97
Reflective subcategory 118
Regular cardinal 268
Regular category 236
Regular epimorphism 136
Replete subcategory 118
Representable functor 9
retract 24
Retraction 24
Right adjoint functor 98
Saturated class 190
Section 24
Separator 151
Set 3
Small category 6
Small set 3
Solution set condition 109
Source of an arrow 5
span 305
Special adjoint functor theorem 110
Split idempotent 271
Stone — Cech compactification 113
Strong epimorphism 137 193
Strong family of generators 152 157
Strong generator 152 157
Strong-epi-mono factorization 148
Subcategory 19
Subobject 132
Suspension 104
Target of an arrow 5
Tensor product of Set-valued functors 129
Terminal object 48
The more general adjoint functor theorem 277
union 133
Universal closure operation 227
Universal colimit 85
Universe 2
Well-powered category 132
Yoneda embedding 17
Yoneda Lemma 11
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