The Stacks project

Lemma 67.45.11. Let $S$ be a scheme. Let $X_ i \to Y$, $i = 1, \ldots , n$ be finite morphisms of algebraic spaces over $S$. Then $X_1 \amalg \ldots \amalg X_ n \to Y$ is finite too.

Proof. Follows from the case of schemes (Morphisms, Lemma 29.44.13) by étale localization. $\square$

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