The Stacks project

Definition 7.45.1. The global sections of a presheaf of sets $\mathcal{F}$ over a site $\mathcal{C}$ is the set

\[ \Gamma (\mathcal{C}, \mathcal{F}) = \mathop{\mathrm{Mor}}\nolimits _{\textit{PSh}(\mathcal{C})}(*, \mathcal{F}) \]

where $*$ is the final object in the category of presheaves on $\mathcal{C}$, i.e., the presheaf which associates to every object a singleton.

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View Definition 7.45.1 as pdf