functor

(redirected from Endofunctor)
Also found in: Dictionary.
Related to Endofunctor: Hilbert space, Monoid, Functors

functor

[′fəŋk·tər]
(computer science)
(mathematics)
A function between categories which associates objects with objects and morphisms with morphisms.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

functor

In category theory, a functor F is an operator on types. F is also considered to be a polymorphic operator on functions with the type

F : (a -> b) -> (F a -> F b).

Functors are a generalisation of the function "map". The type operator in this case takes a type T and returns type "list of T". The map function takes a function and applies it to each element of a list.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in periodicals archive ?
An endofunctor G of C is a monoidal comonad if and only if [G.sub.*] is a bimonoid in F.
When a split epimorphism (f, s) : X [??] Y is algebraically exponentiable, the induced endofunctor [f.sup.*].Of on [Pt.sub.X]C is (up to a natural isomorphism) equal to the endofunctor [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [p.sub.0] and [p.sub.1] are given by the kernel equivalence relation:
(i) The natural morphism of endofunctors of [D.sub.b]([D.sub.X])