The Stacks project

Example 7.10.13. Let $\mathcal{C}$ be a site. Let $E$ be a set. The constant sheaf $\underline{E}$ with value $E$ is the sheafification of the presheaf given by the constant functor with value $E$. It is characterized by the rule $\mathop{\mathrm{Mor}}\nolimits _{\mathop{\mathit{Sh}}\nolimits (\mathcal{C})}(\underline{E}, \mathcal{F}) = \mathop{\mathrm{Mor}}\nolimits _{\textit{Sets}}(E, \Gamma (\mathcal{C}, \mathcal{F}))$ for every sheaf $\mathcal{F}$ on $\mathcal{C}$ where the notation is from Definition 7.45.1.

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