full functor

A functor \(F: \mathcal{C} \rightarrow \mathcal{D}\) on two categories \(\mathcal{C}, \mathcal{D}\) is full, if the induced map between two hom-sets \(F_{A,B}: \mathrm{Hom}_{\mathcal{C}}(A,B) \rightarrow \mathrm{Hom}_{\mathcal{D}}(F(A),F(B))\) is surjective analoguos for a contravariant functor