For locally small category denote by the full subcategory of on small colimits of representables. The category is cocomplete iff the Yoneda embedding has a left adjoint . If has a further left adjoint and is moreover complete, then it is called completely distributive.
Completely distributive categories are an example of continuous algebras for a lax-idempotent 2-monad. (But the condition of being completely distributive seems to be stronger since it also requires completeness.)
Last revised on November 27, 2022 at 05:50:55. See the history of this page for a list of all contributions to it.