Definition 66.7.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.

1. We say $f$ is submersive1 if the continuous map $|X| \to |Y|$ is submersive, see Topology, Definition 5.6.3.

2. We say $f$ is universally submersive if for every morphism of algebraic spaces $Y' \to Y$ the base change $Y' \times _ Y X \to Y'$ is submersive.

[1] This is very different from the notion of a submersion of differential manifolds.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).