covariant functor
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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
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
covariant — adjective (Of a functor) which preserves composition … Wiktionary
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
Delta-functor — In homological algebra, a δ functor between two abelian categories A and B is a collection of functors from A to B together with a collection of morphisms that satisfy properties generalising those of derived functors. A universal δ functor is a… … Wikipedia
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
representable functor — noun Given a category C, a covariant representable functor h sends each object X in category C to C(A,X), the set of arrows from A to X, and sends each arrow f:X rarr; Y to a function from C(A,X) to C(A,Y) which maps each element s of C(A,X) to… … Wiktionary
Yoneda lemma — In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object . It is a vast generalisation of Cayley s theorem from group theory (a group being a particular kind of… … 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
