Situation 21.37.1. Here $(\mathcal{D}, \mathcal{O}_\mathcal {D})$ be a ringed site and $p : \mathcal{C} \to \mathcal{D}$ is a fibred category. We endow $\mathcal{C}$ with the topology inherited from $\mathcal{D}$ (Stacks, Section 8.10). We denote $\pi : \mathop{\mathit{Sh}}\nolimits (\mathcal{C}) \to \mathop{\mathit{Sh}}\nolimits (\mathcal{D})$ the morphism of topoi associated to $p$ (Stacks, Lemma 8.10.3). We set $\mathcal{O}_\mathcal {C} = \pi ^{-1}\mathcal{O}_\mathcal {D}$ so that we obtain a morphism of ringed topoi

\[ \pi : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C}) \longrightarrow (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}_\mathcal {D}) \]

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