nLab
bifunctor

Contents

Disambiguation

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

Definition

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 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.

Examples

Famous bifunctors are


  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.

Revised on September 2, 2012 05:15:23 by Todd Trimble (67.81.93.25)