= Freyd general adjoint functor theorem
{c}
= General adjoint functor theorem
{synonym}
For a <functor> $U:\mathcal C\to\mathcal D$ between <locally small categories>, with $\mathcal C$ a <complete category>, $U$ has a <left adjoint> if and only if it preserves small <categorical limits> and satisfies the <solution-set condition>. The dual statement uses cocompleteness, small-colimit preservation and weakly terminal solution sets to characterize existence of a <right adjoint>.
Back to article page
