The Stacks project

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 4.38.7. $\square$


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