Functor

Noun

1. A function word.
2. A function object.
3. A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.

   "In the category of categories C a t {\displaystyle \mathbf {Cat} } the objects are categories and the morphisms are functors."

4. A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.