The Stacks project

Example 7.33.8. Let $\mathcal{C}$ be a category endowed with the chaotic topology (Example 7.6.6). For every object $U_0$ of $\mathcal{C}$ the functor $u : U \mapsto \mathop{\mathrm{Mor}}\nolimits _\mathcal {C}(U_0, U)$ defines a point $p$ of $\mathcal{C}$. Namely, conditions (1) and (2) of Definition 7.32.2 are immediate as the only coverings are given by identity maps. Condition (2) holds because $\mathcal{F}_ p = \mathcal{F}(U_0)$ and since the topology is discrete taking sections over $U_0$ is an exact functor.