Abstract

A profunctor (also called a distributor or a correspondence) is a functor of two variables F : C x C’—> Set, contravariant in one argument and covariant in the other. I will introduce the (bi)category Prof of profunctors, and work through their composition and unit structure in some detail: although the notation looks somewhat formidable, I hope to show that they are actually quite easy to reason with.

Topics covered: - definition of profunctors, the bicategory Prof - Yoneda reduction for computing coends - profunctor composition and identities

Prerequisites: - a vague memory of coends and Kan extensions will be useful, but not necessary - familiarity with functors and other standard categorical definitions