The Stacks project

Definition 90.3.9. Let $f: B \to A$ be a ring map in $\mathcal{C}_\Lambda$. We say $f$ is an essential surjection if it has the following properties:

1. $f$ is surjective.

2. If $g: C \to B$ is a ring map in $\mathcal{C}_\Lambda$ such that $f \circ g$ is surjective, then $g$ is surjective.