Lemma 7.21.1. Let $\mathcal{C}$ and $\mathcal{D}$ be sites. Let $u : \mathcal{C} \to \mathcal{D}$ be cocontinuous. The functors $g_* = {}_ su$ and $g^{-1} = (u^ p\ )^\# $ define a morphism of topoi $g$ from $\mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ to $\mathop{\mathit{Sh}}\nolimits (\mathcal{D})$.

**Proof.**
This is exactly the content of Lemma 7.20.3.
$\square$

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