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 ( 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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