Lemma 8.7.2 (04ZM)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 8: Stacks
Section 8.7: The inertia stack
Lemma 8.7.2 (cite)

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Lemma 8.7.2. Let $\mathcal{C}$ be a site. If $\mathcal{S}$ is a stack in groupoids, then the canonical $1$ -morphism $\mathcal{I}_\mathcal {S} \to \mathcal{S}$ is an equivalence if and only if $\mathcal{S}$ is a stack in setoids.

Proof. Follows directly from Categories, Lemma 4.39.7. $\square$

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