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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 |
Co-wellpowered category vs. extensions of factorization structures 15.20 15.21
Co-wellpowered category vs. monadic category 20.29
Co-wellpowered category vs. topological category 21.16 21.17
Co-wellpowered category vs. wellpoweredness 12.13
Co-wellpowered category, concrete 8.19
Co-wellpowered functor 8.37
Co-wellpowered functor vs. adjoint functor 18.11 18.14
Co-wellpowered functor vs. essentially algebraic category 23.14
Co-wellpowered functor, concrete 8.37
Co-wellpowered functor, extremal 8.37
Co-wellpowered functor, implies domain is co-wellpowered 8.38
Coarser than, (preorder) relation on concrete functors 5.18
Cocomplete category 12.2 ff
Cocomplete category vs. cartesian closed category 27.4
Cocomplete category vs. colimit-dense subcategory 12.12
Cocomplete category vs. complete category 12.13 25K
Cocomplete category vs. copower 12H
Cocomplete category vs. essentially algebraic category 23.12 23.13
Cocomplete category vs. solid category 25.15 25.16
Cocomplete category vs. topological category 21.16 21.17
Cocomplete category with a small colimit-dense subcategory is complete 12.12
Cocomplete category, almost implies complete 12.7 ff
Cocomplete subcategory, vs. reflective subcategory 12K
Cocone, = natural sink 11.27
Codomain of a function 2.1
Codomain of a morphism 3.2
Codomain of a sink 10.62
Codomain of a source 10.1
Codomain of a structured source 17.1
Coequalizer 7.68 ff
Coequalizer as a colimit 11.28
Coequalizer vs. completeness 12J
Coequalizer vs. epimorphism 7M
Coequalizer vs. forgetful functor 7.73
Coequalizer vs. isomorphism 7.70
Coequalizer vs. monomorphism 7.70
Coequalizer vs. pushout square 11.33
Coequalizer, absolute 20.14
Coequalizer, existence 12.1 15F
Coequalizer, preservation 13.1
Coequalizer, split 20.14
Coequalizer, uniqueness 7.70
Coessential morphism, w.r.t. a class of morphisms 9.27
Coessential quotient map 9.27
Cointersection 11.28
Cointersection vs. (E, M)-category 15.14 15.15 15.16
Cointersection, existence 12.1
Colimit 11.27 ff
Colimit creation 13.17
Colimit preservation 13.1
Colimit preservation vs. topological functor 21.15
Colimit reflection 13.22
Colimit uniqueness 11.29
Colimit vs. (co-)adjoint functor 18D
Colimit vs. coproduct 11.28
Colimit vs. monadic functor 20.13
Colimit vs. reflection arrow 13.30
Colimit, absolute 20.14
Colimit, concrete 13.12
Colimit, detected by regularly monadic functor 20.33
Colimit, detection, = detection of colimit 13.22
Colimit, directed, = directed colimit 11.28
Colimit, domain of 11.27
Colimit, lifting of 13.17
Colimit, lifting of vs. topological functor 21.15
Colimit-closed subcategory, vs. reflective subcategory 13.29
Colimit-dense full embedding, preserves limits 13L
Colimit-dense subcategory 12.10
Colimit-dense subcategory vs. (co)completeness 12.12
Colimit-dense subcategory, embedding of preserves limits 13.11
Comma category 5.38 3K 21F
Commuting triangle and square 3.4
Compact category 18K
Comparison functor 20.37 ff
Comparison functor vs. adjoint functor 20.42
Comparison functor vs. faithful functor 20.43
Comparison functor vs. full functor 20.43 20.44
Complete category 12.2 ff
Complete category and wellpowered category, is strongly complete 12.5
Complete category characterization 12.3
Complete category vs. adjoint functor 18.12 18.14 18.17 18.19
Complete category vs. cocomplete category 12.13 25K
Complete category vs. coequalizer 12J
Complete category vs. colimit-dense subcategory 12.12
Complete category vs. essentially algebraic category 23.12 23.13
Complete category vs. solid category 25.15
Complete category vs. strongly complete category 12.5 12I
Complete category vs. topological category 21.16 21.17
Complete lattice, vs. has products 10.32
Completion, of abstract categories 12L
Completion, regarded as reflection 4.17
Completion, universal 12M
complex numbers 2.1
Composite of (concrete) functors 3.23 5.14
Composite of (concrete) functors vs. natural transformation 6.3
Composite of epimorphisms, is epimorphism 7.41
Composite of essential embeddings 9.14
Composite of functions 2.1
Composite of isomorphisms, is isomorphism 3.14
Composite of monomorphisms, is monomorphism 7.34
Composite of morphisms 3.1
Composite of natural transformations 6.13
Composite of sources 10.3
Composite of sources vs. (E, M)-category 15.5
Composition of morphisms 3.1 ff
Composition of morphisms in a quasicategory 3.49
Composition of morphisms is associative 3.1
Composition of morphisms vs. (E, M)-category 15.14 15.15
Composition of morphisms vs. (E, M)-structured category 14.6
Composition, as a morphism 27E
Concept, (self-)dual 3.7
Concrete adjoint functor, vs. concrete coadjoint functor 21.24
Concrete category 5.1 ff
Concrete category over 1, vs. concrete functors 5.11
Concrete category over Set, = construct 3.3(2) 5.1
Concrete category vs. Cat 5I
Concrete category, (A, U) has property P means A (or U) has property P 5.3
Concrete category, (uniquely) transportable 5.28 5.35 5.36
Concrete category, amnestic modification 5.6 5.33 5.34
Concrete category, amnestic, = amnestic concrete category 5.4 ff
Concrete category, duality principle for 5.20
Concrete category, fibre-complete 5.7 5.42
Concrete category, fibre-discrete 5.7 5.8 5.39
Concrete category, monadic 20.8 ff
Concrete category, solid, = solid concrete category 25.10 ff
Concrete category, strongly fibre-small 26.5
Concrete category, topological, = topological concrete category 21.7 ff
Concrete category, “concretely isomorphic” is stronger than “isomorphic” 5.12
Concrete co-adjoint functor vs. concrete adjoint functor 21.24
Concrete co-adjoint functor vs. Galois correspondence 21E
Concrete co-wellpoweredness 8.19
Concrete co-wellpoweredness vs. extremal co-wellpoweredness 8E
Concrete colimit 13.12
Concrete coproduct 13.12
Concrete coreflector, i.e., coreflector induced by identity-carried coreflection arrows 5.22
Concrete embedding, essential 21J
Concrete equivalence 5.13
Concrete functor 5.9 ff
Concrete functor between algebraic categories is algebraic 23.22
Concrete functor between constructs 5D
Concrete functor between essentially algebraic categories is essentially algebraic 23.17
Concrete functor between regularly algebraic categories is regularly algebraic 23.40
Concrete functor vs. embedding functor and equivalent objects 5.10
Concrete functor vs. monadic category 20E
Concrete functor, composite 5.14
Concrete functor, existence of a concrete natural transformation between 6.24
Concrete functorspecified by its values on objects 5.10 5.11
Concrete generation of an object 8.15
Concrete generation of an object vs. (extremal) generation 8.16
Concrete generation of an object vs. extremal epimorphism 8.18
| Concrete generation of an object vs. universal arrow 8.24
Concrete isomorphism 5.12 5N
Concrete limit 13.12
Concrete limit dense 12M
Concrete limit vs. concrete colimit 13.10
Concrete limit, characterized 13.15
Concrete limit, reflection of 13C
Concrete limit, two step construction 13.16
Concrete natural transformation 6.23
Concrete natural transformation vs. concrete functors 6.24
Concrete product 10.52
Concrete product as a concrete limit 13.12
Concrete product preserved by composition 10.56
Concrete product vs. has M-initial subobjects 21.42
Concrete product vs. initial source 10.53
Concrete product vs. monotopological construct 21.42
Concrete quasitopos, vs. universally topological category 28.18
Concrete reflector vs. concrete functors that are reflectors 5.22
Concrete reflector, = reflector induced by identity-carried reflection arrows 5.22 5E
Concrete subcategory 5.21 ff
Concrete subcategory, concretely (co)reflective, = concretely (co)reflective subcategory 5.22
Concretely cartesian closed category 27.11
Concretely cartesian closed category vs. discrete objects 27.15
Concretely cartesian closed category vs. topological category 27.15
Concretely cartesian closed construct, vs. subconstruct of Set 27.16
Concretely co-wellpowered concrete category 8.19
Concretely co-wellpowered functor 8.37
Concretely co-wellpowered functor vs. (ConGen, Initial Mono-Source) functor 17.11
Concretely complete 12M
Concretely coreflective subcategory 5.22
Concretely coreflective subcategory vs. topological subcategory 21.33
Concretely equivalent, is not symmetric 5.13
Concretely generating structured arrow see Concrete generation of an object
Concretely reflective concrete subcategory 5.22
Concretely reflective concrete subcategory of amnestic category is full 5.24
Concretely reflective concrete subcategory of non-amnestic concrete category need not be full 5.25 4.21
Concretely reflective concrete subcategory vs. finally dense subcategory 21.32
Concretely reflective concrete subcategory vs. initial source 10.50
Concretely reflective concrete subcategory vs. initially closed subcategory 21.31
Concretely reflective concrete subcategory vs. reflector 5.26 5.27 5.31 5.32
Concretely reflective concrete subcategory vs. topological (sub)category 21.32 21.33
Concretizable category 5J 10L
Concretizable category vs. separating set 7Q
Cone, = natural source 11.3
Conglomerate 2.3
Conglomerate of all classes 2.3
Conglomerate of morphisms between two objects in a quasicategory 3.49
Conglomerate of objects in a quasicategory 3.49
Conglomerate, (il)legitimate 2.3
Conglomerate, codability by 2.3
Conglomerate, small 2.3
Congruence fork 20.14
Congruence relation 11.20
Congruence relation vs. equalizer 11.20
Congruence relation vs. monomorphism 11.20 11R
Congruence relation vs. pulation square 11.33
Congruence relation, coequalizer of, vs. monadic construct 20.35
Constant functions are morphisms, vs. has function spaces 27.18
Constant functor 3.20(2)
Constant morphism 7A 10W
Construct 3.3(2) 5.1
Construct must be regular wellpowered and regular co-wellpowered 7.88
Construct not determinated by object class 3.3(2)
Construct, bounded 24.11
Construct, concretely co-wellpowered 8D
Construct, monadic, = monadic construct 20.34 ff
Contraction 3.3(3)
Contravariant exponential functor 27.5
Contravariant exponential functor vs. (co-)adjoint functor 27.7
Contravariant hom-functor 3.20(5)
Contravariant power-set functor 3.20(9)
Copower, of an object 10.63
Copower, of an object vs. cocompleteness 12H
Copower, of an object vs. free object 10R
Copower, of an object, non-existence 10S
Coproduct 10.63 ff
Coproduct of functors 10U
Coproduct vs. colimit 11.28
Coproduct, concrete 13.12
Coproduct, existence 10I 12.1 12G
Coproduct, preservation of 13.1
Coreflection arrow 4.25 ff
Coreflection, Galois 6.26
Coreflective hull, vs. cartesian-closed category 27C
Coreflective modification, of a concrete category 5.22 5K
Coreflective subcategory 4.27 16.1
Coreflective subcategory vs. bicoreflective subcategory 16.4
Coreflective subcategory vs. cartesian closed subcategory 27.9
Coreflector for a coreflective subcategory 4.27
Coreflector, concrete 5.22
Coseparating set 18L
Coseparator 7.16
Coseparator is extremal in balanced category 10.18
Coseparator vs. faithful hom-functor 7.17
Coseparator vs. power of an object 10.38
Coseparator vs. topological category 21.16 21.17
Coseparator, category with, is regular wellpowered and regular co-wellpowered 7.89
Coseparator, extremal 10.17
Costructured arrow 8.40
Costructured sink 17.4
Covariant exponential functor 27.5
Covariant Hom-functor 3.20(4)
Covariant power-set functor 3.20(8)
Cover, projective 9.27
Creation of (Extremal Epi, Mono-Source)- factorizations 23.31
Creation of absolute coequalizers, vs. monadic functor 20.17
Creation of absolute colimits 20.14
Creation of absolute colimits, monadic functor does 20.16
Creation of colimits 13.17
Creation of finite limits, vs. monadic construct 20.35
Creation of isomorphisms 13.35 13M
Creation of isomorphisms vs. creation of limits 13.36
Creation of isomorphisms vs. essentially algebraic functor 23.8
Creation of isomorphisms vs. monadic functor 20.12
Creation of isomorphisms vs. reflection of identities & isomorphisms 13.36
Creation of limits 13.17 13N
Creation of limits vs. creation of isomorphisms 13.36
Creation of limits vs. essentially algebraic functor 23.15
Creation of limits vs. lifts limits uniquely and reflects limits 13.20 13.25
Creation of limits vs. reflection of isomorphisms 13.25
Creation of limits, monadic functor does 20.12
Creation of split coequalizers, vs. monadic functor 20.17
Decomposition of functors 3N
Decomposition of functors vs. factorization structure 26A
Decomposition of Galois correspondence 6.35
Decomposition theorems for solid functors 26.3 26.4
Dense subcategory 12D
Detection and preservation of limits vs. solid functor 25.18 25.19
Detection and preservation of limits vs. topologically algebraic functor 25.18 25.19
Detection of colimits 13.22
Detection of colimits vs. reflective subcategory 13.32
Detection of colimits vs. solid functor 25.14
Detection of limits 13.22
Detection of limits vs. lifting of limits 13.34
Detection of limits vs. solid functor 25.14
Detection of wellpoweredness, vs. monadic functor 20.12
Diagonal 14.1 14B 15.1 15K 17.3 17D
Diagonal morphism 10V 10W
Diagonalization property, (E, M), = (E, M)-diagonalization property 15.1
Diagonalization property, causes E and M to determine each other 15.5
Diagonalization property, w.r.t. a functor 17.3
Diagram, = functor 11.1 ff
Diagram, limit of 11.3
Directed colimit 11.28 11O
Directed colimit vs. finitary quasivariety 24A
Discrete category 3.26
Discrete functor, vs. topological functor 21.12
Discrete object 8.1 8M
Discrete object must be smallest element in the fibre 8.4
Discrete object vs. concretely cartesian closed subcategory 27.15
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