# nLab corepresentable functor

A functor $C \to Set$ is corepresentable if it is (isomorphic to) a functor of the form $Hom_C(c,-)$ for some object $c\in C$.

This is equivalently a representable functor defined on the opposite category $C^{op}$. Often no terminological distinction is made between representable and corepresentable ones (both being called simply “representable”), since a functor $C\to Set$ can only be “corepresentable” while a functor $C^{op}\to Set$ can only be “representable”.

Created on February 17, 2011 18:15:30 by Mike Shulman (71.136.229.247)