The Stacks project

Definition 7.43.2. Let $\mathcal{C}$ be a site. A strictly full subcategory $E \subset \mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ is a subtopos if there exists an embedding of topoi $f : \mathop{\mathit{Sh}}\nolimits (\mathcal{D}) \to \mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ such that $E$ is equal to the essential image of the functor $f_*$.