functor

funktori puhekieltä a function word
puhekieltä a function object
puhekieltä A morphism between two categories which maps objects from the source category to objects of the target category and arrows from the source category to arrows of the target category, in such a way as to preserve domains and codomains (of the arrows), preserve composition, and preserve identity identities.

In the category of categories, \mathbb{CAT}, the objects are categories and the morphisms are functors.