The Stacks project

Definition 7.3.3. We say $\mathcal{F}$ is a subpresheaf of $\mathcal{G}$ if for every object $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$ the set $\mathcal{F}(U)$ is a subset of $\mathcal{G}(U)$, compatibly with the restriction mappings.

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View Definition 7.3.3 as pdf