Adjoint functor theorem
= Adjoint functor theorem
A theorem giving sufficient conditions for a <functor> to have an <adjoint functor>. The <general adjoint functor theorem> uses a <complete category>, <locally small categories>, preservation of <categorical limits> and a <solution-set condition>. The <Special adjoint functor theorem> obtains that condition from a <well-powered> source and a <small cogenerating family>. Precise hypotheses matter in both forms.