Definition 5.46.
Let \(j_*\colon \Uu \hookrightarrow \Xx\) be an open immersion of topoi, and let \(j^*\colon \Xx \to \Uu\) be its left adjoint. We define the closed subtopos complementary to \(\Uu\) as
\[\Xx / \Uu \quad := \quad \{\,X \in \Xx \mid j^*(X) = *\,\} \quad \subseteq \quad \Xx.\]
More generally, we say that a morphism of topoi \(i\colon \Zz \to \Xx\) is a closed immersion if there exists a \((-1)\)-truncated object \(U \in \Xx\) such that \(i_*\colon \Zz \to \Xx\) induces an equivalence \(\Zz \iso \Xx / \Uu\).