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
A bifunctor (short for binary functor, that is -ary) or functor of two variables is simply a functor whose domain is the product of two categories.
For , and categories, a functor
is also called a bifunctor from and to .
Famous bifunctors are
the hom functor
on any locally small category , or if is a closed category, the internal hom functor
on every monoidal category the tensor product functor
A bifunctor of the form is called a profunctor.
bifunctor, two-variable adjunction, Quillen bifunctor
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. ↩
Last revised on December 6, 2022 at 17:48:25. See the history of this page for a list of all contributions to it.