nLab bifunctor




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 22-ary) or functor of two variables is simply a functor whose domain is the product of two categories.

For C 1C_1, C 2C_2 and DD categories, a functor

F:C 1×C 2D F : C_1 \times C_2 \to D

is also called a bifunctor from C 1C_1 and C 2C_2 to DD.


Famous bifunctors are

A bifunctor of the form D op×CSetD^{op} \times C \to Set is called a profunctor.

  1. 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.