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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 |
Natural source 11.3
Natural source is natural transformation 11.5
Natural transformation 6.1 ff
Natural transformation vs. composition of functors 6.3
Natural transformation vs. opposite functor 6.3
Natural transformation vs. Set-valued functor 6.18
Natural transformation, cardinality of 6B
Natural transformation, composition 6.13 6A
Natural transformation, concrete 6.23 6.24
Natural transformation, identity-carried, = concrete natural transformation 6.23
Natural transformation, M-transformation 6.5
Naturality condition 6.1
Naturally isomorphic 6.5
Neighborhood space 5N
Normal monomorphism 7C
Object 3.1 ff
Object class of a category 3.1 3.2
Object class of a category vs. identity morphisms 3.19
Object, copower of 10.63
Object, discrete, = discrete object 8.1
Object, equivalent to another, in a concrete category 5.4
Object, free, = free object 8.22
Object, indiscrete, = indiscrete object 8.3
Object, initial, = initial object 7.1
Object, injective, = injective object 9.1
Object, isomorphic 3.15 3.16
Object, power 27.2
Object, power of 10.37
Object, projective, = projective object 9.27
Object, quotient, = quotient object 7.84 ff
Object, terminal, = terminal object 7.4
Object, zero 7.7 27A
Object-free category 3.53
Object-free category, corresponding to a category 3.54 3.55
Object-free functor 3.55
Opposite category 3.5
Opposite category vs. contravariant hom-functor 3.20(5)
Opposite category vs. contravariant power-set functor 3.20(9)
Opposite category vs. dual functor for vector spaces 3.20(12)
Opposite category vs. Stone-functor 3.20(11)
Opposite category, dually equivalent means opposite category is equivalent 3.38
Opposite functor 3.41
Opposite functor vs. Galois connection 6.27 (2)
Opposite functor vs. natural transformation 6.3
Order on concrete functors 5.18
Order on concrete functors vs. concretely reflective subcategory 5.26
Order on objects, in a concrete category 5.4 5.5
Order preserving map vs. monadic functor 20N
Order preserving map, = morphism in Pos 4.3
Ordered pair of sets 2.1
Partial binary algebra 3.52
Partial binary operation 3.52
Partial morphism 28.1
Point-separating source 10.5
Point-separating source vs. mono-source 10.8 10T
Pointed category 3B 7B
Posets, category of 4.3
Posets, category of, down-directed & up-directed 11.4
Power (of an object) 10.37
Power (of an object) vs. coseparator 10.38
Power (of an object), comparison of 10K
Power (of an object)with discrete exponent is product, vs. cartesian closed topological construct 27.24
Power object 27.2
Power-set functor 3.20(8) 3.20(9)
Power-set functor vs. adjoint functor 18E
Power-set functor, representability of 6F
Power-set monad 20.2
Power-set, = set of all subsets 2.1
Power-set-morphism 28.11
Preimage-morphism 28.11
Preorder relation on the fibres, in a concrete category 5.5
Preordered class, as a category 3.3(4)
Preservation and reflection of mono-sources, vs. free object 18.10
Preservation and reflection vs. monadic functor 20.12
Preservation of coequalizers 13.1
Preservation of colimits 13.1
Preservation of coproducts 13.1
Preservation of equalizers 13.1 13.3
Preservation of extremal epimorphisms, vs. monadic functor 20.50
Preservation of initial sources 10.47
Preservation of initial sources vs. finally dense subcategory 10.71
Preservation of limits & colimits §13
Preservation of limits vs. adjoint functor 18.12 18.14 18.17 18.19
Preservation of limits vs. embedding 13.11
Preservation of limits vs. hom-functor 13.7
Preservation of limits vs. monomorphism & mono-source 13.5
Preservation of limits vs. representable functor 13.9
Preservation of limits vs. solid functor 25.14
Preservation of limits, adjoint functor does 18.9
Preservation of mono-sources, implied by (Generating, —)-factorization for 2-sources 17.12
Preservation of products 13.1 13.3
Preservation of pullbacks 13.3
Preservation of regular epimorphisms, vs. (regularly) monadic functor 20.32 20.50
Preservation of small limits, vs. lift limits 13.19
Preservation of strong limits, vs. (ExtrGen, Mono-Source) functor 17.11 17H
Preservation of terminal object 13.3
Pretopological space 5N
Product (of morphisms) 10.34
Product (of object) with discrete factors are coproducts, vs. cartesian closed topological construct 27.24
Product (of objects) 10.19 ff
Product (of objects) and pullback square, vs. equalizer 11.11 11.14
Product (of objects) existence 10.29 10I 12.1
Product (of objects) for Banach spaces 10J
Product (of objects) in abelian groups 10G
Product (of objects) is extremal mono-source 10.21
Product (of objects) of pairs 10.30
Product (of objects) preserved by first mono-factor 10.56
Product (of objects) vs. (E, M)-structured category 14.15
Product (of objects) vs. empty source 10.20
Product (of objects) vs. equalizer 10.36
Product (of objects) vs. finite product 11B
Product (of objects) vs. first factor 10.25
Product (of objects) vs. hom-functor 10E 10F
Product (of objects) vs. isomorphism 10.20
Product (of objects) vs. projective limit 11B
Product (of objects) vs. pullback square 11.13 11C 11D
Product (of objects) vs. retraction 10.28
Product (of objects) vs. terminal object 10.20 10.30 10H
Product (of objects), characterization 10Q
Product (of objects), composition of 10.25
Product (of objects), concrete, = concrete product 10.52 13.12
Product (of objects), notation for 10.23
Product (of objects), preservation of 13.1
Product (of objects), uniqueness 10.22
Product category 3.3(4)
Product of epimorphisms, vs. cartesian closed category 27.8
Product source, vs. isomorphism 10.26
Projection morphism 10.23
Projection morphism vs. retraction 10.27
Projective cover 9.27
Projective hull, w.r.t. a class of morphisms 9.27
Projective limit 11.4
Projective limit vs. (finite) product 11B
Projective object 9.27
Projective object vs. free object 9.29 9.30
Projective object, extremal, in algebraic category 23.28 23.29
Projective object, regular 9E
Projective object, w.r.t. a class of morphisms 9.27
Proper class 2.2. See also Large category
Proper quasicategory 3.50 3.51
Proper quasicategory, quasicategory of all categories is 3.51
Property of objects, as (isomorphism-closed) full subcategory 4.8
Property, dual 3.7
Property, universal 4.16 4.25
Pulation square 11.32 11Q
Pulation square vs. congruence relation 11.33
Pullback 11.8 ff. See also Pullback square
Pullback of a 2-sink 11.8
Pullback of a morphism 11.8
Pullback of a sink along a morphism 28.13
| Pullback square 11.8 ff. See also Pullback
Pullback square and product vs. equalizer 11.14
Pullback square vs. equalizer and product 11.11
Pullback square vs. extremal mono-source 11.9
Pullback square vs. limit 11.9
Pullback square vs. monomorphism 11.15 11.16
Pullback square vs. product 11.13
Pullback square vs. terminal object 11.13
Pullback square, cancellation of 11.10 11.15
Pullback square, composition of 11.10
Pullback stable 11.17 28.13
Pullback vs. (E, M)-structured category 14.15
Pullback vs. epi-sink 11I
Pullback vs. equalizer 11S
Pullback vs. kernel 11E
Pullback vs. product 11C 11D
Pullback vs. section 11H
Pullback vs. strict monomorphism 11H
Pullback, closure under the formation of 11.17
Pullback, existence 12.1
Pullback, multiple 11L—11N
Pushout 11.30 ff
Pushout of a 2-source 11.30
Pushout square 11.30 ff
Pushout square vs. coequalizer 11.33
Pushout vs. (E, M)-category 15.14 15.15 15.16
Pushout vs. mono-source 11P
Pushout, existence 12.1
Quasicategory 3.49 ff
Quasicategory of all categories, is not a category 3.5 3.51
Quasicategory of all object-free categories 3.55
Quasicategory of all quasicategories, yields Russell-like paradox 3.51 3L
Quasicategory vs. hom-functor 3.51
Quasicategory, (il)legitimate 6.16
Quasicategory, category is 3.51
Quasicategory, functor quasicategory 6.15 6H
Quasicategory, proper 3.50 3.51
Quasicategoryof all concrete categories over a given base category 5.14 5.15
Quasiconstruct of quasitopological spaces 5.6
Quasitopos 28.7
Quasitopos is (Epi, RegMono)-structured 28.10
Quasivariety, = algebraic construct 24.12
Quasivariety, finitary, = finitary quasivariety 16.12
Quotient map 9.27
Quotient map, coessential 9.27
Quotient morphism 8.10
Quotient morphism vs. (regular) epimorphism & retraction 8.12
Quotient morphism vs. extremal epimorphism 23G
Quotient morphism, composition & first factor of 8.13
Quotient object 7.84 ff
Quotient object, extremal, = extremal quotient object 7.84
Quotient object, order on 7.85
Quotient object, regular, = regular quotient object 7.84
Rational & real numbers 2.1
Realization = full, concrete embedding 5O
Reflection See also Reflector
Reflection arrow 4.16 ff
Reflection arrow vs. colimit 13.30
Reflection arrow, uniqueness 4.19
Reflection of (extremal) epimorphisms 17.13
Reflection of (extremal) epimorphisms vs. adjoint situation 19.14
Reflection of (extremal) epimorphisms vs. essentially algebraic functor 23.2
Reflection of (extremal) epimorphisms vs. faithful functor 19.14
Reflection of (extremal) epimorphisms vs. monadic functor 20.12
Reflection of colimits 13.22
Reflection of equalizers 17.13
Reflection of equalizers vs. essentially algebraic functor 23.2
Reflection of equalizers vs. faithful functor 13.24 17.13 17.14
Reflection of equalizers vs. reflection of limits 17.13 17.14
Reflection of identities, vs. creation of isomorphisms 13.36
Reflection of isomorphisms 13.35
Reflection of isomorphisms vs. (Generating, Mono-Source)-factoriza- tions of 2-sources 17.13
Reflection of isomorphisms vs. creation of isomorphisms 13.36
Reflection of isomorphisms vs. creation of limits 13.25
Reflection of isomorphisms vs. essentially algebraic functor 23.2
Reflection of isomorphisms vs. reflection of limits 17.13 17.14
Reflection of isomorphisms, functors need not 3.22
Reflection of limits 13.22 13G 17.13
Reflection of limits vs. essentially algebraic functor 23.2
Reflection of limits vs. lifting of limits 13.23
Reflection of limits vs. mono-sources are initial 17.13 17.14
Reflection of limits vs. reflection of equalizers 17.13 17.14
Reflection of limitsvs, reflection of isomorphisms 17.13 17.14
Reflection of products vs. faithful functor 10.60
Reflection of regular epimorphisms vs. initiality of mono-sources 19.14
Reflection, concrete 5.22 5E
Reflection, Galois 6.26
Reflective embedding, misbehaved 13K
Reflective modification, of a concrete category 5.22 5K
Reflective subcategory 4.16 16D 16E
Reflective subcategory of a functor-structured category, vs. cocomplete category that has free objects 26.8
Reflective subcategory of special categories 4D
Reflective subcategory vs. adjoint situation 19.4
Reflective subcategory vs. cartesian closed subcategory 27.9
Reflective subcategory vs. cocomplete subcategory 12K
Reflective subcategory vs. colimit-closed subcategory 13.29
Reflective subcategory vs. detection of colimits 13.32
Reflective subcategory vs. E-monadic subcategory 20.25
Reflective subcategory vs. injective objects 9.25
Reflective subcategory vs. limits 13.28
Reflective subcategory vs. monadic category 20.18
Reflective subcategory, characterization of fullness 4.20
Reflective subcategory, embedding of, preserves and reflects mono-sources 18.7
Reflective subcategory, full 4.20 7F
Reflective subcategory, intersections 4F
Reflective subcategory, nonfull, with reflection arrows isomorphisms, example 4.21 13K
Reflective subcategory, reflectors are naturally isomorphic 6.7
Reflector (for a reflective subcategory) 4.23 4H
Reflector as composite of epireflectors 16.24
Reflector vs. concretely reflective subcategory 5.26 5.27 5.31 5.32
Reflector, concrete 5.22 5E
Reflector, existence 4.22
Reflector, naturally isomorphic to others 6.7
Reflector, uniqueness 4.24 6.7
Regular category 14E
Regular co-wellpowered category 7.87
Regular co-wellpowered category vs. category with separator or coseparator 7.89
Regular co-wellpowered category vs. construct 7.88
Regular epimorphism 7.71 ff
Regular epimorphism is extremal epimorphism 7.75
Regular epimorphism vs. (E, M)-category 15.7 15.8
Regular epimorphism vs. (E, Mono)-structured category 14.14
Regular epimorphism vs. (extremal) epimorphism 7O 21.13
Regular epimorphism vs. final morphism 8.11(4) 8O 20.51
Regular epimorphism vs. forgetful functor 7.72(5) 7.73
Regular epimorphism vs. monadic functor 20.51 20.52
Regular epimorphism vs. quotient morphism 8.12
Regular epimorphism vs. retraction 7.75
Regular epimorphism, closed under composition, vs. (RegEpi, Mono-Source)-category 15.25
Regular epimorphism, composition of 14.22
Regular epimorphism, preservation and reflection, vs. regularly algebraic category 23.39
Regular epireflective subcategory 16.1
Regular epireflective subconstruct, vs. (regular) equational subconstruct 16.18
Regular equation 16.16
Regular equational subconstruct, vs. regular epireflective subconstruct 16.18
Regular factorization 15.12 20.32
Regular factorization vs. (RegEpi, Mono-Source)-category 15.13
Regular factorization vs. algebraic functor 24.2
Regular factorization vs. regularly algebraic category 23.38 23.39
Regular factorization vs. regularly monadic category 20.30
Regular monomorphism 7.56 ff
Regular monomorphism in functionally Hausdorff spaces 7J
Regular monomorphism in semigroups 14I
Regular monomorphism is (extremal) monomorphism 7.59 7.63
Regular monomorphism is pullback stable 11.18
Regular monomorphism preserved by products 10.35
Regular monomorphism vs. embedding 8.7 8A
Regular monomorphism vs. equalizer 13.6
Regular monomorphism vs. extremal monomorphism 7.62 7.63 7.65 7J 12B 14.20 14I 21.13
Regular monomorphism vs. monomorphism 7O
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