The Stacks project

Lemma 8.12.3. Let $u : \mathcal{C} \to \mathcal{D}$ be a continuous functor of sites. Let $p : \mathcal{S} \to \mathcal{D}$ be a stack in groupoids over $\mathcal{D}$. Then $u^ p\mathcal{S}$ is a stack in groupoids over $\mathcal{C}$.

Proof. This follows immediately from Lemma 8.12.2 and the fact that all fibre categories are groupoids. $\square$

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