A functor $F\colon \mathcal{C}\to \mathcal{D}$ is essentially surjective1 if it satisfies the following condition:
- For each $D\in \text{Obj}\webleft (\mathcal{D}\webright )$, there exists some object $A$ of $\mathcal{C}$ such that $F\webleft (A\webright )\cong D$.
1Further Terminology: Also called an eso functor, where the name “eso” comes from essentially surjective on objects.
