The Stacks project

Remark 7.7.2. If the covering $\{ U_ i \to U\} _{i \in I}$ is the empty family (this means that $I = \emptyset $), then the sheaf condition signifies that $\mathcal{F}(U) = \{ *\} $ is a singleton set. This is because in (7.7.1.1) the second and third sets are empty products in the category of sets, which are final objects in the category of sets, hence singletons.

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