corepresentable functor

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

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

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