This article is about functors of two variables. Possibly the term ‘bifunctor’ has been used for a functor between bicategories (citation?), but such usage (if it exists) seems to be rare; the usual term for that is ‘pseudo functor’.1
For for , and categories, a functor
is also called a bifunctor from and to .
Famous bifunctors are
the hom functor
Outside of certain computer science contexts, it is not clear that the term ‘bifunctor’ is used frequently nowadays, even for the sense of a functor of two variables. It is used more frequently in older texts. ↩