A connection between the notions of “algebraically complete” and “algebraically compact” category is considered. The notions were introduced by P. Freyd. In the first case, every functor should have a least fixpoint, and in the second, a least and the largest fixpoint, that canonically coincide. It is shown that 1) several interesting categories are algebraically \(\omega\)-complete and 2) categories enriched over complete partial orders are “almost” \(\omega\)-compact: each localy-continuous functor has a canonical fixpoint.