The Stacks project

Definition 7.52.1. Let $\mathcal{C}$ be a category. Let $J$ be a topology on $\mathcal{C}$. A point $p$ of the topology is given by a functor $u : \mathcal{C} \to \textit{Sets}$ such that

1. For every covering sieve $S$ on $U$ the map $S_ p \to (h_ U)_ p$ is surjective.

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