The Stacks project

Definition 87.30.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of formal algebraic spaces over $S$. Let $\Delta _{X/Y} : X \to X \times _ Y X$ be the diagonal morphism.

  1. We say $f$ is separated if $\Delta _{X/Y}$ is a closed immersion.

  2. We say $f$ is quasi-separated if $\Delta _{X/Y}$ is quasi-compact.

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View Definition 87.30.1 as pdf