The Stacks project

Definition 101.11.2. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks.

  1. We say $f$ is open if the map of topological spaces $|\mathcal{X}| \to |\mathcal{Y}|$ is open.

  2. We say $f$ is universally open if for every morphism of algebraic stacks $\mathcal{Z} \to \mathcal{Y}$ the morphism of topological spaces

    \[ |\mathcal{Z} \times _\mathcal {Y} \mathcal{X}| \to |\mathcal{Z}| \]

    is open, i.e., the base change $\mathcal{Z} \times _\mathcal {Y} \mathcal{X} \to \mathcal{Z}$ is open.

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View Definition 101.11.2 as pdf