nLab
representable functor theorem

The representable functor theorem

Statement

The representable functor theorem states that a Set-valued functor on a complete category is representable if and only if it is continuous and has a solution set?.

As representable functors are ubiquitous, this theorem is essentially equivalent to the adjoint functor theorem and to theorems guaranteeing the existence of limits.

Created on October 8, 2011 12:40:28 by Toby Bartels (216.170.5.99)