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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 |
Discrete object vs. topological category 21.11
Discrete quasicategory 3.51
Discrete space functor, is a full embedding 3.29
Discrete terminal object, vs. has function spaces 27.18
Disjoint union, of a family of sets 2.1
Dispersed factorization structure 15L
Distributive law for cartesian closed category 27.8
Domain of a diagram, = scheme 11.1
Domain of a function 2.1
Domain of a morphism 3.2
Domain of a sink 10.62
Domain of a source 10.1
Domain of a structured source 17.1
Dominion 14J
Down-directed poset 11.4
Dual category, = opposite category 3.5
Dual concept, of a “categorical concept” 3.7
Dual functor, = opposite functor 3.41
Dual of a categorical statement involving functors 3.40 3.42
Dual property 3.7
Dual statement, of a “categorical statement” 3.7
Duality principle for categories 3.7 3E
Duality principle for concrete categories 5.20
Duality principle for topological category 21.10
Duality theories, vs. representability 10N
Dually equivalent categories 3.37 3.38
E-equation 16.16
E-equational subcategory 16.16
E-equational subcategory vs. closed under the formation of Msources and E-quotients 16.17
E-equational subcategory vs. closed under the formation of products 16.17
E-implicational subcategory 16.12
E-implicational subcategory vs. E-reflective subcategory 16.14
E-monad 20.21 ff
E-monadic functor 20.21 ff
E-monadic functor lifts (E, M)-factorizations uniquely 20.24
E-monadic functor vs. reflective subcategory 20.25
E-reflective hull, = smallest E-reflective subcategory 16.21
E-reflective hull, characterization of members 16.22
E-reflective subcategory 16.1
E-reflective subcategory vs. closure under the formation of M-sources 16.8
E-reflective subcategory vs. E-implicational subcategory 16.14
E-reflective subcategory vs. E-monadic functor 20.25
E-reflective subcategory, intersection of 16.20
Eilenberg — Moore category 20.4
Elementhood-morphism 28.11
Embeddable, fully 4.6
Embedding functor 3.27
Embedding functor closed under composition and first factor 3.30
Embedding functor is (up to isomorphism) inclusion of subcategory 4.5
Embedding functor vs. faithful functor 3.28 4.5
Embedding functor vs. full functor 3.29
Embedding functor vs. preservation of limit 13.11
Embedding functor, finally dense 10.72
Embedding morphism 8.6 ff
Embedding morphism in Cat 8C
Embedding morphism vs. monomorphism 8.7
Embedding morphism vs. regular monomorphism 8.7 8A
Embedding morphism vs. section 8.7
Embedding morphism, composition 8.9
Embedding morphism, essential 9.12
Embedding morphism, first factor of 8.9
Embedding, Yoneda 6.19 6J
Empty category 3.3(4)
Empty source 10.2
Empty source vs. product 10.20
Enough injectives 9.9
Enough injectives vs. absolute retract 9.10
Enough injectives vs. injective hull 9D
Epi-sink 10.63
Epi-sink vs. pullback 11I
Epi-transformation 6.5 7R
Epi-transformation vs. adjoint situation 19.14
Epimorphism 7.38 ff
Epimorphism as extremal monomorphism is isomorphism 7.66
Epimorphism as section is isomorphism 7.43
Epimorphism for groups 7H
Epimorphism vs. (E, M)-category 15.8 15.14 15.15
Epimorphism vs. (E, M)-structured category 14.10
Epimorphism vs. coequalizer 7M
Epimorphism vs. equalizer 7.54
Epimorphism vs. generating structured arrows 8.16 8.18 8.36
Epimorphism vs. hom-functor 19C
Epimorphism vs. quotient morphism 8.12
Epimorphism vs. regular epimorphism 7O
Epimorphism vs. retraction 7.42
Epimorphism, closed under composition 7.41
Epimorphism, equals implication 16.12
Epimorphism, extremal, = extremal epimorphism 7.74
Epimorphism, preserved and reflected by equivalence functor 7.47
Epimorphism, products of 10D
Epimorphism, reflected by faithful functor 7.44
Epimorphism, regular, = regular epimorphism 7.71
Epimorphism, split, = retraction 7.24
Epimorphism, stable 11J
Epimorphism, swell 7.76 15A
Epimorphism, types 7.76
Epireflective hulls, vs. co-wellpoweredness 16C
Epireflective subcategory 16.1 ff
Epireflective subcategory vs. closure under the formation of products and extremal subobjects 16.9 16.10
Epireflective subcategory vs. extremal mono-source 16H
Epireflective subcategory vs. strongly limit-closed subcategory 16L
Epireflective subcategory with bad behavior 16A
Epireflective subcategory, regular 16I
Equalizer 7.51 ff
Equalizer and product vs. (Epi, ExtrMono)-structured category 14.19
Equalizer and product vs. congruence relation 11.20
Equalizer and product vs. epimorphism and isomorphism 7.54
Equalizer and product vs. product and pullback square 10.36 11.14 11S
Equalizer and product vs. regular monomorphism 13.6
Equalizer and product, reflection of 17.13
Equalizer and product, uniqueness 7.53
Equalizer and product, vs. pullback square 11.11 11.14
Equalizer, existence 12.1
Equalizer, preservation of 13.1 13.3
Equation, = regular implication with free domain 16.16
Equational subcategory 16.16
Equational subcategoryof  , char 16.19
Equational subconstruct, vs. epireflective subconstruct 16.18
Equivalence functor is topologically algebraic 25.2
Equivalence functor vs. adjoint situation 19.8 19H
Equivalence functor vs. natural isomorphism 6.8
Equivalence functor, = full, faithful, and isomorphism-dense functor 3.33 3H
Equivalence functor, concrete 5.13
Equivalence functor, preserves and reflects special morphisms 7.47
Equivalence functor, properties of 3.36
Equivalence of quasicategories 3.51
Equivalence of “standard” and “object-free” versions of category theory 3.55
Equivalence relation on a conglomerate 2.3
Equivalence, natural, = natural isomorphism 6.5
Equivalent categories 3.33
Equivalent categories vs. isomorphic categories 3.35
Equivalent categories, dually 3.37 3.38
Equivalent objects, in a concrete category 5.4
Essential embedding 9.12
Essential embedding, properties of 9.14
Essential extension 9.11 9H
Essential extension vs. injective object 9.15
Essential extension, types of 9.20
Essential morphism, w.r.t. a class of morphisms 9.22
Essential uniqueness, of universal arrow 8.25 8.35
Essentially algebraic category 23.5 ff
Essentially algebraic category has coequalizers 23.10
Essentially algebraic category vs. co-wellpoweredness 23.14
Essentially algebraic category vs. completeness & cocompleteness 23.12 23.13
Essentially algebraic category vs. monadic category 23.16
Essentially algebraic category vs. wellpoweredness 23.12 23.13
Essentially algebraic category, characterization 23.8
Essentially algebraic category, concrete functor between 23.17
Essentially algebraic category, implies embeddings = monomorphisms 23.7
Essentially algebraic embedding 23B
| Essentially algebraic functor 23.1 ff
Essentially algebraic functor detects colimits 23.11
Essentially algebraic functor is faithful adjoint functor 23.3
Essentially algebraic functor is topologically algebraic 25.2
Essentially algebraic functor preserves and creates limits 23.11
Essentially algebraic functor vs. creates limits 23.15
Essentially algebraic functor vs. monadic functor 23C
Essentially algebraic functor vs. solid functor 26.3
Essentially algebraic functor, closed under composition 23.4
Essentially algebraic functor, equivalent conditions 23.2
Evaluation morphism 27.2
Exact category 14F
Exponential functors 27.5
Exponential law for cartesian closed category 27.8
Exponential morphism 27.2
Extension of a factorization structure 15.19 ff
Extension of a factorization structure vs. has products 15.19 15.21
Extension of a factorization structure, equivalent conditions for 15.20
Extension of an object 8.6
Extension, injective 9.11
Extensional topological construct & hull 28B 28C
Extremal co-wellpoweredness 7.87 ff 23I
Extremal co-wellpoweredness detected by regularly monadic functor 20.31
Extremal co-wellpoweredness vs. concrete co-wellpoweredness 8E
Extremal co-wellpoweredness vs. monadic category 20.48
Extremal coseparator 10.17
Extremal coseparator, characterization 10B 10C
Extremal epi-sink 10.63
Extremal epimorphism 7.74 ff
Extremal epimorphism vs. (E, M)-category 15.8
Extremal epimorphism vs. (E, M)-structured category 14.12 14.13 14.14
Extremal epimorphism vs. concrete generation 8.18
Extremal epimorphism vs. extremally generating structured arrows 8.16 8.18 8.36
Extremal epimorphism vs. final morphism 8.11(5)
Extremal epimorphism vs. pullbacks and products 23.28 23.29
Extremal epimorphism vs. quotient morphism in algebraic category 23.26 23G
Extremal epimorphism vs. regular epimorphism 7.75 21.13
Extremal epimorphism vs. topological category 21.13
Extremal epimorphism, preservation & reflection of vs. regularly algebraic category 23.38
Extremal epimorphism, preservation & reflection of vs. regularly monadic category 20.30
Extremal epimorphism, reflection of 17.13
Extremal epimorphismis final morphism in algebraic category 23.23
Extremal generation of an object 8.15
Extremal generation of an object vs. concrete generation 8.16
Extremal generation of an object vs. extremal epimorphism 8.16 8.18
Extremal mono-source 10.11 ff
Extremal mono-source not preserved by composition 10.14 7N
Extremal mono-source preserved by first factor 10.13
Extremal mono-source vs. (E, M)-category 15.8
Extremal mono-source vs. epireflective subcategory 16H
Extremal mono-source vs. extremal monomorphism 10.26
Extremal mono-source vs. product 10.21
Extremal mono-source vs. pullback square 11.9
Extremal mono-source vs. subsource 10.15
Extremal mono-source, characterization 10A
Extremal monomorphism 7.61 ff
Extremal monomorphism as epimorphism is isomorphism 7.66
Extremal monomorphism preserved by solid functors 25.21
Extremal monomorphism vs. (E, M)-diagonalization property 14.18
Extremal monomorphism vs. (E, M)-structured category 14.10
Extremal monomorphism vs. adjoint functor 18J
Extremal monomorphism vs. balanced category 7.67
Extremal monomorphism vs. extremal mono-source 10.26
Extremal monomorphism vs. monadic functor 20O
Extremal monomorphism vs. regular monomorphism 7.62 7.63 12B 14.20 14I 21.13
Extremal monomorphism vs. topological category 21.13
Extremal monomorphism, closure under composition and intersections 14.18
Extremal monomorphism, composite need not be extremal 7N
Extremal monomorphism, products of 10D
Extremal partial morphism 28.1
Extremal quotient object 7.84
Extremal reducibility of final sinks 28.19
Extremal separator 10.63
Extremal separator characterization 10B 10C
Extremal subobject 7.77
Extremal-subobject classifier 28.11
Extremally co-wellpowered category 7.87
Extremally co-wellpowered category vs. (E, M)-category 15.25 15.26
Extremally co-wellpowered category vs. algebraic category 23.27
Extremally co-wellpowered functor 8.37
Extremally epireflective subcategory 16.1 ff
Extremally epireflective subcategory vs. algebraic subcategory 23.33
Extremally epireflective subcategory, characterization 16M
Extremally generating structured arrow 8.15
Extremally generating structured arrow with respect to a functor 8.30
Extremally monadic construct, is topologically algebraic 25.2
Extremally monadic functor 20M 23N
Extremally projective object 23H
Extremally reducible conglomerate of sinks 28.13
Extremally wellpowered category 7.82 ff
Extremally wellpowered category vs. wellpowered category 7.83
Factorization lemma 14.16
Factorization structure 15.1 ff
Factorization structure for 2-sources 15I
Factorization structure for empty sources 15.2 15G
Factorization structure for morphisms 14.1 ff 14A
Factorization structure for morphisms, extension of, to a factorization structure for sources 15.24
Factorization structure for sinks 15.2
Factorization structure for small sources 15J
Factorization structure vs. decomposition of functors 26A
Factorization structure vs. monadic category 20.28
Factorization structure, dispersed 15J
Factorization structure, extensions of 15.19 ff
Factorization structure, inheritance 16B
Factorization structure, w.r.t. a functor 17.3
Factorization structure, w.r.t. a functor, existence 17C
Factorization structure, w.r.t. a functor, two methods 17.5
Faithful functor 3.27 ff 7G
Faithful functor means epimorphisms are generating 8.32
Faithful functor reflects epimorphisms 7.44
Faithful functor reflects mono-sources 10.7
Faithful functor reflects monomorphisms 7.37
Faithful functor vs. (E, M)-factorization 17.15 17.16
Faithful functor vs. adjoint situation 19.14
Faithful functor vs. comparison functor 20.43
Faithful functor vs. concrete functor 5.10
Faithful functor vs. embedding functor 3.28 3.29 4.5
Faithful functor vs. essentially algebraic functor 23.2
Faithful functor vs. inclusions of subcategories 4.5
Faithful functor vs. initial source 10.59
Faithful functor vs. reflection of (extremal) epimorphisms 19.14
Faithful functor vs. reflection of equalizers 13.24 17.13 17.14
Faithful functor vs. reflection of products 10.60
Faithful functor vs. reflection of special morphisms 17G
Faithful functor vs. solid functor 25.12
Faithful functor vs. thin category 3.29 3G
Faithful functor vs. topologically algebraic functor 25.3
Faithful functor, characterization 8N
Faithful functor, closed under composition 3.30
Faithful functor, is isomorphism iff full and bijective on objects 3.28
Faithful functor, monadic functor is 20.12
Faithful functor, topological functor is 21.3
Fibre of a base object 5.4 5A
Fibre of a base object, largest element need not be discrete 8.5
Fibre of a base object, order on 5.4
Fibre-complete concrete category 5.7
Fibre-complete concrete category, functor-structured categories are 5.42
Fibre-discrete concrete category, categories of T-algebras are 5.39
Fibre-discrete concrete category, concrete category is, iff forgetful functor reflects identities 5.8
Fibre-discrete concrete category, means fibres are ordered by equality 5.7
Fibre-small concrete category 5.4 5.6
Fibre-small concrete category, monadic category is 20.12
Fibre-small topological category 21.34 ff 21B
Final lift, vs. topological category 21.34
Final morphism 8.10 ff
Final morphism is extremal epimorphism in algebraic category 23.23
Final morphism vs. extremal epimorphism 8.11(5)
Final morphism vs. isomorphism 8.14
Final morphism vs. monadic category 20.28
Final morphism vs. regular epimorphism 8.11(4) 8O 20.51
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