- theory of functors
- мат.теория функторов
English-Russian scientific dictionary. 2008.
theory of functors
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Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… … Wikipedia
End (category theory) — Not to be confused with the use of End to represent (categories of) endomorphisms. In category theory, an end of a functor is a universal dinatural transformation from an object e of X to S. More explicitly, this is a pair (e,ω), where e is an… … Wikipedia
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
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
Tilting theory — It turns out that there are applications of our functors which make use of the analogous transformations which we like to think of as a change of basis for a fixed root system a tilting of the axes relative to the roots which results in a… … 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
Monad (category theory) — For the uses of monads in computer software, see monads in functional programming. In category theory, a branch of mathematics, a monad, Kleisli triple, or triple is an (endo )functor, together with two natural transformations. Monads are used in … Wikipedia
Timeline of category theory and related mathematics — This is a timeline of category theory and related mathematics. By related mathematics is meant first hand * Homological algebra * Homotopical algebra * Topology using categories, especially algebraic topology * Categorical logic * Foundations of… … Wikipedia
Outline of category theory — The following outline is provided as an overview of and guide to category theory: Category theory – area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as… … Wikipedia
Nerve (category theory) — In category theory, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C … 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
