Adamek J., Herrlich H., Stecker G.E. — Abstract and Concrete Categories - The Joy of Cats :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

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Предметный указатель

Topological concrete category, duality for      21.9
Topological concrete category, fibre-small      21.34 ff
Topological concrete category, fibre-small reflective subcategory, vs. solid strongly fibre-small category      26.7
Topological concrete category, fibre-small, characterization of      22.3 22.4 22.8
Topological concrete category, fibre-small, vs. closure under the formation of indiscrete objects, initial subobjects, and products      21.37
Topological concrete category, subcategory of, vs. solid category      26.2
Topological construct vs. forgetful functor      21L
Topological construct, fibre-small, characterization of      22.4
Topological functor      21.1 ff
Topological functor is (co-)adjoint      21.12
Topological functor is faithful      21.3
Topological functor is topologically algebraic      25.2
Topological functor lifts limits and colimits      21.15
Topological functor preserves and reflects mono-sources and epi-sinks      21.13
Topological functor preserves limits and colimits      21.15
Topological functor vs. amnestic concrete category      21.5
Topological functor vs. bimorphism      21M
Topological functor vs. discrete and indiscrete functors      21.12
Topological functor vs. indiscrete structures      21.18 21.19 21.20
Topological functor vs. solid functor      26.1 26.3 26.4
Topological functor vs. topologically algebraic functor      25B
Topological functor vs. unique lifting of limits      21.18 21.20
Topological functor vs. uniquely transportable concrete category      21.5
Topological functor, composition of      21.6
Topological structure theorem      22.3
Topological subcategory      21.29 ff
Topological subcategory vs. concretely (co)reflective subcategory      21.33
Topological theory      22B
Topological universe      28.21
Topological universe, equivalent conditions      28.22
Topologically algebraic category      25.1 ff
Topologically algebraic category vs. universal initial completion      25H
Topologically algebraic category, characterization theorem      25.6
Topologically algebraic functor      25.1 ff
Topologically algebraic functor almost is solid      25.18 25.19
Topologically algebraic functor composites yield solid functor      26.1
Topologically algebraic functor is composite of other types      26B
Topologically algebraic functor is faithful and adjoint      25.3
Topologically algebraic functor is solid      25.11
Topologically algebraic functor vs. adjoint functor      25.3 25.6 25.19
Topologically algebraic functor vs. detection and preservation of limits      25.18 25.19
Topologically algebraic functor vs. solid functor      25D 25E
Topologically algebraic functor vs. topological functor      25B
Topology, three approaches      5N
Topos      28.7
Topos is balanced quasitopos      28.8
Topos vs. regular monomorphism      28F
Topos, characterization      28E
Total category      6I
Transformation, natural, = natural transformation      6.1 ff
Transportable concrete category      5.28
Transportable concrete category vs. amnestic concrete category      5.29 5.30
Transportable concrete category vs. concrete category      5.35 5.36
Transportable functor vs. lifting of limits      13E
Transportable functor, monadic functor is      20.12
Triangle, commutes      3.4
Trivial factorization structure      15.3
Trivial monad      20.2

Underlying function      see Forgetful functor
Underlying functor, = forgetful functor      3.20(3) 5.1
Union, of a family of sets      2.1
Unique diagonalization property      14.1 15.1
Unique lifting of limits, vs. topological functor      21.18 21.20
Uniquely transportable concrete category      5.28
Uniquely transportable concrete category vs. topological functor      21.5
Uniquely transportable functor vs. algebraic functor      23.30
Uniquely transportable functor vs. regularly algebraic category      23.38
Unit ball functor      5.2
Unit existence condition      see Object-free category
Unit of a partial binary algebra      3.52 19J
Unit of an adjunction      19.3
Universal arrow      8.22
Universal arrow must be extremally generating      8.33
Universal arrow vs. co-universal arrow      19.1 19.2
Universal arrow vs. concrete generation      8.24
Universal arrow, uniqueness      8.25 8.35
Universal category      4J
Universal completion      12M
Universal initial completion      21I
Universal initial completion vs. topologically algebraic category      25H
Universal property      4.16 4.25 8.22 8.30
Universal structured arrow      8.30
Universally initial morphism      10P
Universally topological category      28.16
Universally topological category as injective object      28G
Universally topological category vs. concrete quasitopos      28.18
Universe      2.2
Up-directed poset      11.4
Upper semicontinuity, as adjointness      18F
Varietal category & functor      23F
Varietor      20.53
Varietor vs. colimits of $\omega$ -chains      20P
Varietor vs. free monad & monadic category      20.56—20.58
Variety, = monadic construct      24.12
Variety, bounded, vs. bounded monadic construct      24.11
Variety, finitary, = finitary variety      16.16 20.20
Variety, vs. equational subquasiconstruct of some $\mathrm{Alg}(\Omega)      24.11
Weak terminal object, vs. terminal object      12.9
Weakly algebraic functor      23A
Weakly terminal set of objects      12F
Well-fibred construct      27.20
Well-fibred topological construct vs. cartesian closed construct      27.22
Wellpowered category      7.82 ff
Wellpowered category and complete category, is strongly complete      12.5
Wellpowered category is regular wellpowered and extremally wellpowered      7.83
Wellpowered category vs. adjoint functor      18.19
Wellpowered category vs. co-wellpoweredness      12.13
Wellpowered category vs. essentially algebraic category      23.12 23.13
Wellpowered category vs. free object      18.10
Wellpowered category vs. topological category      21.16 21.17
Word-monad      20.2
Yoneda embedding      6J
Yoneda Lemma      6.19
Zero morphism      7A
Zero object      7.7
Zero object vs. Cartesian closed category      27A

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