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Adamek J., Herrlich H., Stecker G.E. — Abstract and Concrete Categories - The Joy of Cats
Adamek J., Herrlich H., Stecker G.E. — Abstract and Concrete Categories - The Joy of Cats

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Название: Abstract and Concrete Categories - The Joy of Cats

Авторы: Adamek J., Herrlich H., Stecker G.E.

Язык: en

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 524

Добавлена в каталог: 22.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(ConGen, Initial Mono-Source)-factorizable category      17J
(ConGen, Initial Mono-Source)-functor, vs. concretely co-wellpowered      17.11
(E, $\mathbf M$)-diagonalization property      15.1
(E, $\mathbf M$)-factorization      15.1
(E, M)-category      15.1
(E, M)-category vs. (E, M)-factorization      15.10
(E, M)-category vs. (E, M)-functor      17.4
(E, M)-category vs. co-wellpowered category      15.25 15.26
(E, M)-category vs. extremally co-wellpowered category      15.25 15.26
(E, M)-category vs. mono-source      15.6—15.9
(E, M)-category vs. regular epimorphism      15.7
(E, M)-category vs. strongly complete category      15.25 15.26
(E, M)-category vs. topological category      21.14
(E, M)-category, conditions on E      15.14 15.15
(E, M)-category, consequences of      15.5
(E, M)-category, implies $E \subseteq \mathrm{Epi}$      15.4
(E, M)-category, values for E and M      15.8
(E, M)-diagonalization property      14.1
(E, M)-factorization      14.1
(E, M)-factorization vs. (E, M)-category      15.10
(E, M)-factorization vs. (E, M)-structured category      14.7
(E, M)-factorization vs. faithful functor      17.15 17.16
(E, M)-factorization vs. topological category      21.16 21.17
(E, M)-factorization, uniqueness      15.5
(E, M)-functor vs. (E, M)-category      17.4
(E, M)-functor vs. has (E, M)-factorizations      17.10
(E, M)-functor vs. topologically algebraic functor      25.6
(E, M)-functor, = adjoint functor      17.3 18.3 18.4
(E, M)-functor, implies $E \subseteq \mathrm{Gen}$      17.6
(E, M)-functor, implies factorizations are essentially unique      17.7
(E, M)-functor, implies M determines E      17.7
(E, M)-functor, M need not be closed under composition nor determined by E      17.8
(E, M)-functor, not every functor is      17.4
(E, M)-functor, properties of      17E
(E, M)-structured category      14.1 ff
(E, M)-structured category vs. (E, M)-factorization property      14.7
(E, M)-structured category vs. (extremal) epimorphisms      14.10—14.14
(E, M)-structured category vs. composition of morphisms      14.6
(E, M)-structured category vs. extremal monomorphisms      14.10
(E, M)-structured category vs. isomorphisms      14.5
(E, M)-structured category, consequences of      14.6 14.9 14.11
(E, M)-structured category, duality for      14.3
(E, M)-structured category, relationship to limits      14.15 ff
(E, M)-structured category, relationship to special morphisms      14.10 ff
(E, M)-structured category, uniqueness of factorizations      14.4
(E, Mono)-structured category, vs. regular epimorphism      14.14
(E, Mono-Source)-category, vs. (Epi, M)-category      15.11
(E, Mono-Source)-functor, implies $E\subseteq\mathrm{ExtrGen}$      17.9
(E, —)-category      15B 15D
(E, —)-functor      17.4
(E, —)-structured category      14H
(Epi, ExtrMono)-structured category vs. equalizer      14.19
(Epi, ExtrMono)-structured category vs. intersection      14.19
(Epi, ExtrMono-Source)-category, characterization      15.16
(Epi, ExtrMono-Source)-category, strongly complete category is      15.17
(Epi, ExtrMono-Source)-category, vs. (ExtrEpi, Mono-Source)-category      15C
(Epi, Initial Source)-factorizable category vs. topologically algebraic category      25.6
(Epi, M)-category, characterization      15.16
(Epi, M)-category, characterization vs. (E, Mono-Source)-category      15.11
(Epi, Mono-Source)-factorizable category vs. algebraic category      23.30 23.31
(Epi, Mono-Source)-factorizable category vs. essentially algebraic category      23.8 23.9
(Epi, Mono-Source)-factorizations vs. monadic category      20.49
(Epi, Mono-Source)-factorizations, imply (ExtrEpi, Mono-Source)-category      15.10
(ExtrEpi, Mono-Source)-category vs. (Epi, ExtrMono-Source)-category      15C
(ExtrGen, Mono)-factorization      17I
(ExtrGen, Mono-Source)-functor      17K
(ExtrGen, Mono-Source)-functor vs. preservation of strong limits      17.11 17H
(Generating, M)-functor vs. adjoint functor      18.4
(Generating, Mono-Source)-factorizations of 2-sources vs. reflection of isomorphisms      17.13
(Generating, —)-factorizable functor, composites of      17B
(Generating, —)-factorization, for 2-sources implies preservation of mono-sources      17.12
(RegEpi, Mono)-structured category      14.22 14D
(RegEpi, Mono-Source)-category vs. regular factorization      15.13
(RegEpi, Mono-Source)-category, characterization      15.25
(Strongly Generating, Initial Source)-functor, is topologically algebraic functor      25.6
Absolute coequalizer      20.14
Absolute colimit      20.14
Absolute retract      9.6
Absolute retract vs. enough injectives      9.10
Adjoint functor      18.1 ff
Adjoint functor theorem, concrete      18.19
Adjoint functor theorem, first      18.12
Adjoint functor theorem, special      18.17
Adjoint functor vs. (Generating, M)-functor      18.4
Adjoint functor vs. adjoint situation      19.1 19.4 19.8
Adjoint functor vs. algebraic category      23.31
Adjoint functor vs. co-adjoint functor      18A 19.1
Adjoint functor vs. co-wellpoweredness      18.11 18.14 18.19
Adjoint functor vs. colimit      18D
Adjoint functor vs. completeness      18.12 18.14 18.17 18.19
Adjoint functor vs. essentially algebraic functor      23.8
Adjoint functor vs. exponential functor      27.7
Adjoint functor vs. extremal monomorphism      18J
Adjoint functor vs. free object      18.19
Adjoint functor vs. full, faithful functor      19I
Adjoint functor vs. monadic category      20.46
Adjoint functor vs. monadic functor      20.12 20.17
Adjoint functor vs. reflection of epimorphisms      18I 19B
Adjoint functor vs. regularly algebraic category      23.38
Adjoint functor vs. representable functor      18C
Adjoint functor vs. solid functor      25.12 25.19
Adjoint functor vs. topologically algebraic functor      25.3 25.6 25.19
Adjoint functor vs. wellpoweredness      18.19
Adjoint functor, between posets      18H
Adjoint functor, characterization theorems      18.12 18.14 18.17 18.19
Adjoint functor, characterizations      18.3
Adjoint functor, comparison functor for      20.38 20.42
Adjoint functor, composition of      18.5
Adjoint functor, monadic functor is      20.12
Adjoint functor, preserves mono-sources and limits      18.6 18.9
Adjoint functor, smallness conditions for      18B
Adjoint sequence      19F
Adjoint situation      19.3 ff
Adjoint situation gives rise to a monad      20.3
Adjoint situation induced by (co-)adjoint functor      19.7
Adjoint situation uniqueness      19.9
Adjoint situation vs. adjoint functor      19.1 19.4 19.8
Adjoint situation vs. equivalence functor      19.8 19H
Adjoint situation vs. free object      19.4
Adjoint situation vs. Galois correspondence      19.8
Adjoint situation vs. indiscrete structure      21A
Adjoint situation vs. monad      20A
Adjoint situation vs. reflective subcategory      19.4
Adjoint situation vs. universal arrow      19.7
Adjoint situation, alternative description      19A
Adjoint situation, associated with a monad      20.7
Adjoint situation, composition of      19.13
Adjoint situation, consequences of      19.14
Adjoint situation, duality for      19.6
Adjoint situation, lifting of      21.26 21.28
Adjoint, for a functor      19.10
Algebra, partial binary      3.52
Algebraic category      23.19 ff 23D
Algebraic category vs. (Epi, Mono-Source)-factorizable category      23.30 23.31
Algebraic category vs. adjoint functor      23.31
Algebraic category vs. extremal co-wellpoweredness      23.27
Algebraic category vs. extremal epimorphism      23.30
Algebraic category vs. unique lift of (ExtrEpi, Mono-Source)-factorizations      23.31
Algebraic category, characterization theorem for      23.30 23.31
Algebraic category, concrete functor between      23.22
Algebraic category, implies extremal epimorphisms are final      23.23
Algebraic construct vs. monadic construct      23.41
Algebraic construct, = regular epireflective subconstruct of monadic construct      24.3
Algebraic construct, bounded, vs. bounded quasivariety      24.11
Algebraic functor      23.19 ff
Algebraic functor, closed under composition      23.21
Algebraic functor, need not preserve regular epimorphisms      23.25 23J
Algebraic functor, reflects regular epimorphisms      23.24
Algebraic functor, restrictions of      23L
Algebraic functor, vs. composite of regular monadic functors      24.2
Algebraic functor, vs. regular epimorphism      23J
Algebraic functor, vs. regular factorization      24.2
Algebraic functor, vs. uniquely transportable functor      23.30
Algebraic hull of a concrete category      23K
Algebraic subcategory vs. extremally epireflective subcategory      23.33
Algebraic subcategory, conditions for      23.32 23.33
Algebraic theory      20C
Algebraic-topological decompositions      26C
Algebraic-type functors, relationships among      23.42
Amnestic concrete category      5.4 ff
Amnestic concrete category vs. Galois correspondence      6.29—6.36
Amnestic concrete category vs. topological functor      21.5
Amnestic concrete category vs. transportable concrete category      5.29 5.30
Amnestic functor      3.27 5.6 13.21 13.25 13.28
Amnestic modification, of a concrete category      5.6 5.33 5.34 5F
Amnesticity, vs. lifting of limits      13.21
Arrow category      3K 6.17
Arrow, co-universal, = co-universal costructured arrow      8.40
Arrow, costructured, = costructured arrow      8.40
Arrow, reflection, = reflection arrow      4.16
Arrow, structured, = structured arrow      8.15
Arrow, universal, = universal structured arrow      8.22
Associativity, composition of morphisms has      3.1 3.53 3C
Axiom of Choice      2.3 9A
Axiom of replacement      2.2
Axiom, topological      22.6
Balanced category      7.49 ff
Balanced category vs. extremal monomorphism      7.67
Balanced category vs. mono-source      10.12
Balanced category, topological, scarcity of      21N
Base category      5.1 ff
Bicoreflective subcategory vs. coreflective subcategory      16.4
Bicoreflective subcategory vs. separator      16.4
Bimorphism      7.49
Bimorphism vs. topological functor      21M
Bireflective subcategory      16.1
Bireflective subcategory, monoreflective subcategory is      16.3
Birkhoff-theorem      16G
Boolean ring      3.26 footnote
Cartesian closed category      27.1 ff
Cartesian closed category vs. coreflective hull      27C
Cartesian closed category vs. products of epimorphisms      27.8
Cartesian closed category vs. zero object      27A
Cartesian closed category, characterization theorem      27.4
Cartesian closed construct      27.16 ff 27D
Cartesian closed construct vs. well-fibred topological construct      27.22
Cartesian closed subcategory      27.9
Cartesian closed subcategory vs. (co)reflective subcategory      27.9
Cartesian closed topological category as injective object      27F
Cartesian closed topological category, implies base category is cartesian closed      27.14
Cartesian closed topological construct vs. powers with discrete exponents (resp. factors)      27.24
Cartesian closed topological hull      27G
Cartesian product of sets      2.1
Categorical statement involving functors, dual of      3.40 3.42
Category      3.1 ff
Category of all categories, can’t be formed because of set-theoretical restrictions      3.48
Category of concrete categories      5.15 5C
Category of objects over (resp. under) an object      3K
Category of small categories      3.47
Category of small categories is a large category      3.48
Category of small categories vs. concrete category      5I
Category of type 2      3C
Category theory, “object-free version”      3.55
Category with all products must be thin      10.32
Category, (co)complete, = (co)complete category      12.2
Category, (E, M), = (E, M)-category      15.1 ff
Category, (E, —)-structured      14H
Category, algebraic, = algebraic category      23.19 ff
Category, alternative definition      3C
Category, arrow      3K
Category, base, = base category      5.1 ff
Category, cartesian closed, = cartesian closed category      27.1
Category, co-wellpowered, = co-wellpowered category      7.87
Category, comma      3K 5.38 21F
Category, compact      18K
Category, concretely cartesian closed, = concretely cartesian closed category      27.11
Category, concretizable      5J
Category, discrete      3.26
Category, dual, = opposite category      3.5
Category, Eilenberg-Moore      20.4
Category, empty      3.3(4)
Category, essentially algebraic, = essentially algebraic category      23.5 ff
Category, exact      14F
Category, extremally co-wellpowered, = extremally co-wellpowered category      7.87
Category, extremally wellpowered, = extremally wellpowered category      7.82
Category, finitary      24.4 24.7
Category, finitely (co)complete      12.2
Category, free      3A
Category, functor-costructured      5.43
Category, functor-structured, = functor-structured category      5.40
Category, graph of      3A
Category, is a quasicategory      3.51
Category, isomorphic      3.24
Category, Kleisli      20.39 20B
Category, large      3.44
Category, locally presentable      20H
Category, monadic, = monadic category      20.8 ff
Category, non-co-wellpowered      7L
Category, object-free, = object-free category      3.53
Category, opposite, = opposite category      3.5
Category, pointed      3B 7B
Category, product      3.3(4)
Category, regular co-wellpowered      7.87—7.89
Category, regular wellpowered      7.82 7.88 7.89
Category, regularly algebraic, = regularly algebraic category      23.35 ff
Category, skeleton of a      4.12—4.15 4I
Category, small      3.44—3.45
Category, solid, = solid category      25.10 ff
Category, strongly (co)complete, = strongly (co)complete category      12.2
Category, sub-      see Subcategory
Category, terminal      3.3(4)
Category, thin      3.26 3.29 3G
Category, topological, = topological category      21.7 ff
Category, topologically algebraic, = topologically algebraic category      25.1 ff
Category, total      6I
Category, universal      4J
Category, universally topological      28.16 28.18 28G
Category, wellpowered, = wellpowered category      7.82
Choice, axiom of      2.3 9A
class      2.2
Class as a category, (is not a construct)      3.3(4)
Class of all sets, = universe      2.2
Class, large, = proper class      2.2
Class, preordered      3.3(4)
Class, proper      2.2
Class, small, = set      2.2
Closed under the formation of intersections      11.26
Closed under the formation of M-sources      16.7
Closed under the formation of M-sources and E-quotients, vs. E-equational subcategory      16.17
Closed under the formation of M-sources vs. E-reflective      16.8
Closed under the formation of products and extremal subobjects, vs. (epi)reflective subcategory      16.9 16.10
Closed under the formation of products vs. E-equational subcategory      16.17
Closed under the formation of pullbacks      11.17
Closure space      5N
Co-      see Dual concept
Co-adjoint functor      18.1 ff
Co-adjoint functor vs. adjoint functor      18A 19.1 19.2 19.11
Co-adjoint functor vs. colimit      18D
Co-adjoint functor vs. contravariant exponential functor      27.7
Co-adjoint, for a functor      19.10
Co-axiom, topological      22.6
Co-unit of an adjunction      19.3 19J
Co-universal arrow      8.40
Co-universal arrow vs. universal arrow      19.1 19.2
Co-wellpowered category      7.87 ff
Co-wellpowered category vs. (E, M)-category      15.25 15.26
Co-wellpowered category vs. adjoint functor      18.11 18.14 18.19
Co-wellpowered category vs. cartesian closed category      27.4
Co-wellpowered category vs. epireflective hulls      16C
Co-wellpowered category vs. essentially algebraic category      23.14
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