Lemma 94.17.1 (04WZ)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 94: Algebraic Stacks
Section 94.17: The algebraic stack associated to a smooth groupoid
Lemma 94.17.1 (cite)

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Lemma 94.17.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ . Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over $S$ . Then the diagonal of $[U/R]$ is representable by algebraic spaces.

Proof. It suffices to show that the $\mathit{Isom}$ -sheaves are algebraic spaces, see Lemma 94.10.11. This follows from Bootstrap, Lemma 80.11.5. $\square$

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