# nLab representable functor theorem

The 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.

Last revised on April 3, 2020 at 14:38:18. See the history of this page for a list of all contributions to it.