The Stacks project

Lemma 87.12.4. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of formal algebraic spaces over $S$ which is representable by algebraic spaces. Then $f$ is surjective in the sense of Bootstrap, Definition 80.4.1 if and only if $f_{red} : X_{red} \to Y_{red}$ is a surjective morphism of algebraic spaces.

Proof. Omitted. $\square$

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