The Stacks project

Definition 7.43.6. Let $\mathcal{C}$ be a site. A strictly full subcategory $E \subset \mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ is an closed subtopos if there exists a subsheaf $\mathcal{F}$ of the final object of $\mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ such that $E$ is the subtopos described in Lemma 7.43.5.

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