A functor $F\colon \mathcal{C}\to \mathcal{D}$ is surjective on objects if the action on objects
\[ F\colon \operatorname {\mathrm{Obj}}(\mathcal{C})\to \operatorname {\mathrm{Obj}}(\mathcal{D}) \]
of $F$ is surjective.
11.8.2 Surjective on Objects Functors
Let $\mathcal{C}$ and $\mathcal{D}$ be categories.
