The Stacks project

Definition 7.43.4. Let $\mathcal{C}$ be a site. A strictly full subcategory $E \subset \mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ is an open 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 $\mathop{\mathit{Sh}}\nolimits (\mathcal{C})/\mathcal{F}$ described in Lemma 7.43.3.