topological closure of a category

Dear all, I have the following situation and I'd like to know whether there is a name for it, or whether someone knows examples like that. That would be helpful. 1) a locally presentable category C 2) a topological locally presentable category D 3) a left adjoint F:C-->D 4) F is faithful but not full (i.e. one-to-one on morphisms) and essentially surjective. So F is not an equivalence of categories. Could D be a kind of "topological closure" of C ? Thanks in advance. pg.