The Stacks project

Definition 17.4.5. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_ X$-modules. Given a set $I$, and local sections $s_ i$, $i \in I$ of $\mathcal{F}$ we say that the subsheaf $\mathcal{G}$ of Lemma 17.4.4 above is the subsheaf generated by the $s_ i$.

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View Definition 17.4.5 as pdf