Definition 7.17.
Let \((E,E^{\corp})\) be a fractured topos. A morphism \(f\colon Y\to X\) in \(E\) is admissible if, for every map \(j_!U\to X\) with \(U\in E^{\corp}\), the pullback
\[Y\times_Xj_!U\longrightarrow j_!U\]
belongs to the image of \(E^{\corp}_{/U}\to E_{/j_!U}\). This determines a wide subcategory \(E^{\ad}\subseteq E\).