essentially surjective

Definition

Given categories $\mathcal{C}$ and $\mathcal{D}$, a functor $F:\mathcal{C}\to \mathcal{D}$ is called essentially surjective if for all $Z\in \mathcal{D}$ there exists an $X\in \mathcal{C}$ such that $F(X)$ and $Z$ are isomorphic in $\mathcal{D}$.