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The Stacks project

Lemma 8.13.1. Let $\mathcal{C}$ be a site. Let $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Then $j_ U : \mathcal{C}/U \to \mathcal{C}$ is a stack over $\mathcal{C}$ if and only if $h_ U$ is a sheaf.

Proof. Combine Lemma 8.6.3 with Categories, Example 4.38.7. $\square$

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View Lemma 8.13.1 as pdf