- functors
- Функторы
Большой англо-русский и русско-английский словарь. 2001.
functors
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Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Image functors for sheaves — In mathematics, especially in sheaf theory, a domain applied in areas such as topology, logic and algebraic geometry, there are four image functors for sheaves which belong together in various senses.Given a continuous mapping f : X rarr; Y of… … Wikipedia
Full and faithful functors — In category theory, a faithful functor (resp. a full functor) is a functor which is injective (resp. surjective) when restricted to each set of morphisms with a given source and target.Explicitly, let C and D be (locally small) categories and let … Wikipedia
Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… … Wikipedia
Derived functor — In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… … Wikipedia
Fibred category — Fibred categories are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull backs) of objects such as vector bundles … Wikipedia
Natural transformation — This article is about natural transformations in category theory. For the natural competence of bacteria to take up foreign DNA, see Transformation (genetics). In category theory, a branch of mathematics, a natural transformation provides a way… … Wikipedia
Function object — A function object, also called a functor or functional, is a computer programming construct allowing an object to be invoked or called as if it were an ordinary function, usually with the same syntax.Function objects are unrelated to functors in… … Wikipedia
Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… … Wikipedia
Derived category — In mathematics, the derived category D(C) of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C. The construction proceeds on the… … Wikipedia
Limit (category theory) — In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint… … Wikipedia
