Solution set condition

Summary

The solution set condition on a functor $G \colon \mathcal{D} \to \mathcal{C}$ asks the following. For each object $c$, a mere set of morphisms $c \to G d$ is enough to factor all of them. It is a smallness condition. Together with completeness and preservation of limits, it gives the existence of a left adjoint in Freyd's adjoint functor theorem.