[002W] Definition 4.4.2·a (Definable class in a fibration).

Let $E$ be a cartesian fibration over $B$. A definable class $\mathfrak{F}$ in $E$ is a stable subcollection of the displayed objects of $E$ such that for any $\bar{u}\in E\Sub{u}$, there exists a cartesian map $\bar{v}\to \bar{u}$ lying over a monomorphism $v\rightarrowtail u$ such that $\bar{v}\in \mathfrak{F}$ and, moreover, any cartesian morphism $\bar{w}\to\bar{u}$ such that $\bar{w}\in\mathfrak{F}$ factors through $\bar{v}\to\bar{u}$.