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The Stacks project

Lemma 37.67.4. In Situation 37.67.1. If $X$ and $Y$ are separated, then the pushout $Y \amalg _ Z X$ (Proposition 37.67.3) is separated. Same with “separated over $S$”, “quasi-separated”, and “quasi-separated over $S$”.

Proof. The morphism $Y \amalg X \to Y \amalg _ Z X$ is surjective and universall closed. Thus we may apply Morphisms, Lemma 29.41.11. $\square$

Comments (1)

Comment #9450 by Ivan on

Typo in the proof: says "universall" instead of "universally"

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  • 5 comment(s) on Section 37.67: Pushouts in the category of schemes, II

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