Definition 7.32.2. Let $\mathcal{C}$ be a site. A *point $p$ of the site $\mathcal{C}$* is given by a functor $u : \mathcal{C} \to \textit{Sets}$ such that

For every covering $\{ U_ i \to U\} $ of $\mathcal{C}$ the map $\coprod u(U_ i) \to u(U)$ is surjective.

For every covering $\{ U_ i \to U\} $ of $\mathcal{C}$ and every morphism $V \to U$ the maps $u(U_ i \times _ U V) \to u(U_ i) \times _{u(U)} u(V)$ are bijective.

The stalk functor $\mathop{\mathit{Sh}}\nolimits (\mathcal{C}) \to \textit{Sets}$, $\mathcal{F} \mapsto \mathcal{F}_ p$ is left exact.

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