Representable functor — In mathematics, especially in category theory, a representable functor is a functor of a special form from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i … Wikipedia
Functor category — In category theory, a branch of mathematics, the functors between two given categories can themselves be turned into a category; the morphisms in this functor category are natural transformations between functors. Functor categories are of… … 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
Hom functor — In mathematics, specifically in category theory, Hom sets, i.e. sets of morphisms between objects, give rise to important functors to the category of sets. These functors are called Hom functors and have numerous applications in category theory… … Wikipedia
Exact functor — In homological algebra, an exact functor is a functor, from some category to another, which preserves exact sequences. Exact functors are very convenient in algebraic calculations, roughly speaking because they can be applied to presentations 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
Diagonal functor — In category theory, for any object a in any category where the product exists, there exists the diagonal morphism satisfying for , where πk … Wikipedia
Subfunctor — In category theory, a branch of mathematics, a subfunctor is a special type of functor which is an analogue of a subset. Definition Let C be a category, and let F be a functor from C to the category Set of all sets. A functor G from C to Set is a … 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
Brown's representability theorem — In mathematics, Brown s representability theorem in homotopy theory gives necessary and sufficient conditions on a contravariant functor F on the homotopy category Hot of pointed CW complexes, to the category of sets Set, to be a representable… … Wikipedia
