The Stacks project

Definition 101.12.2. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks.

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

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

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

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View Definition 101.12.2 as pdf