Functor

In category theory a functor is a mapping from one category to another which maps objects to objects and morphisms to morphisms in such a manner that the composition of morphisms and the identities are preserved. For the precise definition and examples, see the article on category theory.

Functors were first considered in [algebraic topology]?, where algebraic objects are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps. Nowadays, functors are used throughout modern mathematics to relate various categories.