  We study codensity monads $T$ induced by (mostly small, mostly dense) full
subcategories $A \subset K$. These monads behave quite similarly, we show some
connections with the Isbell duality, pro-finite objects and compact spaces. We
prove that they are quite unlikely to be accessible. Finally, we introduce the
notion of generically idempotent monad and comment its properties.

Category Theory;General Topology;Logic