Lemma 18.36.1. Let $\mathcal{C}$ be a site. Let $p$ be a point of $\mathcal{C}$.

We have $(\mathcal{F}^\# )_ p = \mathcal{F}_ p$ for any presheaf of sets on $\mathcal{C}$.

The stalk functor $\mathop{\mathit{Sh}}\nolimits (\mathcal{C}) \to \textit{Sets}$, $\mathcal{F} \mapsto \mathcal{F}_ p$ is exact (see Categories, Definition 4.23.1) and commutes with arbitrary colimits.

The stalk functor $\textit{PSh}(\mathcal{C}) \to \textit{Sets}$, $\mathcal{F} \mapsto \mathcal{F}_ p$ is exact (see Categories, Definition 4.23.1) and commutes with arbitrary colimits.

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