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| Авторизация |
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| Adamek J., Herrlich H., Stecker G.E. — Abstract and Concrete Categories - The Joy of Cats |
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| Предметный указатель |
Final morphism, composition of 8.13
Final morphism, first factor of 8.13
Final morphism, products of 28J
Final quotient object 8.10
Final sink 10.63 ff
Final sink, reducibility of, vs. representable partial morphisms 28.15
Finally closed subcategory 21.29
Finally closed subcategoryvs. concretely coreflective subcategory 22.8
Finally dense embedding 10.72
Finally dense subcategory 10.69
Finally dense subcategory vs. concretely reflective subcategory 21.32
Finally dense subcategory vs. preserves initial sources 10.71
Finally dense subcategory vs. topological category 21.32
Finer than, (preorder) relation on concrete functors 5.18
Finitary category 24.4
Finitary category, = finitary variety, if monadic 24.7
Finitary functor 24.4
Finitary monad 24.4
Finitary quasivariety 16.12
Finitary quasivariety vs. directed colimit 24A
Finitary quasivariety vs. finitary variety 16K 16N 24.9
Finitary quasivariety, = finitary and algebraic category 24.9
Finitary quasivariety, = regular epireflective subconstruct of some finitary monadic construct 24.9
Finitary quasivariety, axiomatic descriptions 23.30 23.31 23.38 24.9 24.10
Finitary quasivariety, characterization theorem 24.9
Finitary variety 16.16
Finitary variety is monadic 20.20
Finitary variety vs. finitary quasivariety 16K 16N 24.9
Finitary variety vs. monadic category 24.7
Finitary variety, axiomatic descriptions 20.35 23.40 24.7 24.8
Finitary variety, characterization theorem for 24.7
Finite product 10.29
Finite product vs. product and projective limit 11B
Finitely (co)complete category 12.2
Finitely (co)complete category, characterization 12.4
Finitely complete category, vs. has finite products and representable M-partial morphisms 28.5 28.6
Forgetful functor 3.20(3) 5.1
Forgetful functor vs. coequalizer 7.73
Forgetful functor vs. regular epimorphism 7.73
Forgetful functor vs. topological construct 21L
Fork, congruence 20.14
Fork, split 20.14
Frame 5L 8G
Free automata 8P
Free category 3A
Free functor 19.4
Free monad 20.55
Free monad vs. varietor 20.56 20.57 20.58
Free object 8.22 8F—8L
Free object vs. adjoint functor 18.19
Free object vs. adjoint situation 19.4
Free object vs. copower 10R
Free object vs. initial object 8.23
Free object vs. monomorphism 8.28 8.29
Free object vs. projective object 9.29 9.30
Free object vs. representable forgetful functor 8.23
Free object vs. wellpoweredness 18.10
Free object, existence 18.15
Free object, retract of 9.29
Free objectvs. preservation and reflection of mono-sources 18.10
Full embeddability of familiar constructs 4.7 4K
Full embedding functor 4.6
Full embedding functor vs. comparison functor 20.44
Full embedding functor vs. inclusion of a full subcategory 4.5 4.6
Full faithful functor reflects isomorphisms 3.32
Full faithful functor vs. adjoint situation 19.14
Full faithful functor, is isomorphism iff bijective on objects 3.28
Full faithful functor, properties of 3.31
Full functor 3.27 ff
Full functor closed under composition 3.30
Full functor vs. comparison functor 20.43
Full functor, second factor of is not always full 3.30
Full reflective embedding is topologically algebraic 25.2
Full reflective embedding vs. solid functor 26.1
Full reflective subcategory, characterization 4.20
Full subcategory 4.1 ff 4C
Full subcategory vs. concretely reflective subcategory of amnestic category 5.24
Full subcategory, isomorphism-closed 4.9 4B
Full subcategory, isomorphism-dense 4.9
Function between classes 2.2
Function between conglomerates 2.3
Function between sets 2.1
functor 3.17 ff
Functor quasicategory 6.15 6H
Functor quasicategory, full embedding of any category into 6.20
Functor vs. reflection of identities 3D
Functor, (E, M), = (E, M)-functor 17.3 ff
Functor, (E, —), = (E, —)-functor 17.4
Functor, adjoint, = adjoint functor 18.1 ff
Functor, algebraic, = algebraic functor 23.19 ff
Functor, as family of functions between morphism classes 3.19
Functor, between quasicategories 3.51
Functor, co-adjoint, = co-adjoint functor 18.1 ff
Functor, co-wellpowered, implies domain co-well- powered 8.37 8.38
Functor, comparison, = comparison functor 20.37 ff
Functor, composite of 3.23
Functor, concretely co-wellpowered 8.37
Functor, constant functor 3.20(2)
Functor, contravariant hom-functor 3.20(5)
Functor, contravariant power-set functor 3.20(9)
Functor, coproduct of 10U
Functor, coreflector for a coreflective subcategory 4.27
Functor, covariant hom-functor 3.20(4)
Functor, covariant power-set functor 3.20(8)
Functor, decomposition of 3N
Functor, discrete space 3.29
Functor, dual, = opposite functor 3.41
Functor, duality functor for vector spaces 3.20(12)
Functor, E-monadic, = E-monadic functor 20.21 ff
Functor, embedding, = embedding functor 3.27
Functor, equivalence, = equivalence functor 3.33
Functor, essentially algebraic, = essentially algebraic functor 23.1 ff
Functor, exponential 27.5
Functor, extremally co-wellpowered 8.37
Functor, faithful, = faithful functor 3.27
Functor, finitary 24.4
Functor, forgetful functor, = underlying or forgetful functor 3.20(3) 5.1
Functor, free 19.4
Functor, full, = full functor 3.27
Functor, fundamental group 3.22
Functor, identity 3.20(1)
Functor, inclusion 4.4
Functor, indiscrete space 3.29 21.12
Functor, inverse 3.25
Functor, is embedding iff faithful and injective on objects 3.28
Functor, is isomorphism iff full, faithful, and bijective on objects 3.28
Functor, isomorphism 3.24
Functor, isomorphism-dense 3.33
Functor, M-topological 21K
Functor, monadic, = monadic functor 20.8 ff
Functor, n-th power functor 3.20(10)
Functor, naturally isomorphic to idA 6D
Functor, need not reflect isomorphisms 3.22
Functor, notation 3.18
Functor, object-free 3.55
Functor, object-part determined by the morphism-parts 3.19
Functor, opposite, = opposite functor 3.41
Functor, preserves isomorphisms 3.21
Functor, regularly algebraic, = regularly algebraic functor 23.35 ff
Functor, regularly monadic, = regularly monadic functor 20.21 ff
Functor, representable, = representable functor 6.9
Functor, solid, = solid functor 25.10 ff
Functor, Stone-functor 3.20(11)
Functor, topological, = topological functor 21.1 ff
Functor, topologically algebraic, = topologically algebraic functor 25.1 ff
Functor, underlying, = forgetful functor 3.20(3) 5.1
Functor-costructured category 5.43
Functor-structured category 5.40 6C 28K
Functor-structured category, cartesian closed 27I
Functor-structured category, characterization 22A
| Functor-structured category, reflective subcategory of vs. solid strongly fibre-small category 26.7
Functors, relationships among 25.22
Galois adjoint, = residual functor 6.25
Galois adjunction 19D
Galois co-adjoint, = residuated functor 6.25
Galois connection 6.26 6G
Galois connection, composition of 6.27(1)
Galois connection, dual of 6.27(2)
Galois coreflection 6.26 6.35
Galois correspondence 6.25 19E
Galois correspondence between amnestic concrete categories 6.29—6.36
Galois correspondence for constructs 6.26
Galois correspondence theorem 21.24
Galois correspondence vs. adjoint situation 19.8
Galois correspondence vs. concrete co-adjoint 21E
Galois correspondence vs. initial source preservation 10.49 21.24
Galois correspondence, decomposition of 6.35
Galois correspondence, equivalently described 6.28
Galois isomorphism 6.26 6.35
Galois reflection 6.26
Galois reflection vs. decomposition of Galois correspondence 6.35
Galois reflection, characterization 6.34
Generating structured arrow 8.15 ff
Generating structured arrow, characterization 17A
Generating structured arrow, concretely 8.15
Generating structured arrow, extremally 8.15
Generating structured arrow, strongly generating structured arrow is 25.5
Generating structured arrow, w.r.t. a functor 8.30
Generation vs. concrete generation 8.16
Generation vs. epimorphism 8.16 8.18
Graph of a category 3A
Has (E, M)-factorizations vs. (E, M)-functor 17.10
Has (E, M)-factorizations vs. adjoint functor 18.3
Has (E, M)-factorizations, w.r.t. a functor 17.3
Has (finite) (co)intersections 12.1
Has (finite) (co)products 10.29 12.1
Has a separator, vs. cartesian closed category 27.4
Has coequalizers 12.1
Has coequalizers vs. regularly algebraic category 23.38
Has concrete (co)limits 13.12
Has concrete products 10.54
Has enough injectives 9.9 9.22
Has equalizers 12.1
Has equalizers and (finite) products, means (finitely) complete 12.3 12.4
Has finite intersections and finite products, means finitely complete 12.4
Has finite intersections and products, means complete 12.3
Has finite products, and representable M-partial morphisms vs. finitely complete 28.5 28.6
Has free objects 8.26
Has function spaces 27.17
Has function spaces vs. constant functions are morphisms 27.18
Has function spaces vs. discrete terminal objects 27.18
Has function spaces vs. topological category 27.22
Has limits, vs. (E, M)-structured 14.17
Has M-initial subobjects, vs. concrete products 21.42
Has products 10.29
Has products and equalizers (resp. intersections), means complete 12.3
Has products of all sizes, implies thin category 10.32
Has products vs. extension of factorization structure 15.19 15.21
Has pullbacks 12.1
Has pullbacks and a terminal object, means finitely complete 12.4
Has pushouts 12.1
Has regular factorizations 15.12
Has regular factorizations vs. regularly monadic functor 20.32
Has representable, consequences of 28.3
Has representable, M-partial morphisms 28.1
Has small concrete colimits, characterized 13.14
Hewitt, E. see Duality principle
Hom-functor 3.20(4) 3.20(5)
Hom-functor preserves limits 13.7
Hom-functor vs. (co)separator 7.12 7.17
Hom-functor vs. epimorphism 19C
Hom-functor vs. limit 13H
Hom-functor vs. product 10E 10F
Hom-functor vs. quasicategory 3.51
Hom-functor vs. set-valued functor 6.18
Hull, algebraic 23K
Hull, E-reflective, = E-reflective hull 16.21
Hull, injective 9.16
Idempotent monad 20F
Identity functor 3.20(1) 5.14
Identity morphism 3.1 ff
Identity morphism in a category, as unit in the corresponding object-free category 3.54
Identity morphism vs. isomorphism 3.13
Identity morphism vs. object 3.19
Identity morphism vs. subcategory 4A
Identity morphism, reflection 3D
Identity natural transformation 6.6
Identity-carried A-morphism 5.3
Identity-carried reflection arrow see Concretely reflective concrete subcategory
Illegitimate conglomerate 2.3
Illegitimate quasicategory 6.16
Image of the indexing function 2.1
Image, inverse 11.19
Implication, = epimorphism 16.12
Implication, satisfaction of 16.12
Implicational subcategory 16.12
Inclusion functor 4.4
Indiscrete object 8.3
Indiscrete object must be largest element in the fibre 8.4
Indiscrete object preservation 21.23
Indiscrete object vs. initial source 10.42
Indiscrete object vs. initial subobjects 21.35
Indiscrete object vs. topological category 21.11 21.35
Indiscrete space functor is a full embedding 3.29
Indiscrete space functor vs. topological functor 21.12
Indiscrete structure vs. adjoint situation 21A
Indiscrete structure vs. topological functor 21.18 21.19 21.20
Inductive limit 11.28
Initial completion 21G
Initial lift, vs. topological category 21.34
Initial morphism 8.6
Initial morphism vs. injective morphism 8B
Initial morphism vs. isomorphism 8.14
Initial morphism, composition of 8.9
Initial morphism, first factor of 8.9
Initial morphism, universally 10P
Initial object 7.1
Initial object vs. free object 8.23
Initial object vs. limit 11A
Initial object, uniqueness 7.3
Initial source 10.41
Initial source preservation 10.47
Initial source preservation vs. Galois correspondence 21.24
Initial source preserved by composition 10.45
Initial source preserved by first factor 10.45
Initial source vs. concrete product 10.53
Initial source vs. concretely reflective subcategory 10.50
Initial source vs. faithful functor 10.59
Initial source vs. finally dense subcategory 10.69
Initial source vs. indiscrete object 10.42
Initial source vs. initial subsource, in a fibre-small topological category 21.36
Initial source vs. mono-source 17.13
Initial source vs. subsource 10.46
Initial source w.r.t. a functor 10.57
Initial source, composition of 10O
Initial source, domain of 10.43
Initial subobject 8.6
Initial subobject vs. indiscrete object 21.35
Initial subobject vs. monotopological construct 21.42
Initial subobject vs. topological category 21.35
Initial T-algebra 20I
Initiality-preserving concrete functor, preserves indiscrete objects 21.23
Initially closed subcategory 21.29
Initially closed subcategory of a topological category is topological 21.30
Initially closed subcategory vs. concretely reflective subcategory 21.31 22.3 22.4
Initially dense subcategory 10.69
Injection morphism 10.63
Injective automata 9I
Injective extension 9.11
Injective extension, types of 9.20
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