Equivalently, a functor $F$ is codense iff $Id_B$, together with identity natural transformation $Id_F\colon F \to F$, is the pointwise Kan extension of $F$ along $F$.

Also, $F$ is codense iff its codensity monad is the identity.

A subcategory is codense if the inclusion functor is codense.

Examples

Let $I$ denote the unit interval. Then the full subcategory of the category of compact topological spaces $T$ whose only object is $I^2$ is a dense subcategory of $T$ (Ulmer 68, p.80).