Lemma 67.10.9 (06RV)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.10: Monomorphisms
Lemma 67.10.9 (cite)

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Lemma 67.10.9. Let $S$ be a scheme. If $X \to Y$ is a monomorphism of algebraic spaces over $S$ , then $|X| \to |Y|$ is injective.

Proof. Immediate from the definitions. $\square$

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