Definition 4.42.
Let \(T\) be a topos. We write
\[\Fam(T) := \Ar^{\pb}(T)\]
for the wide subcategory of \(\Ar(T)\) whose morphisms are pullback squares. We call an object \(u\colon E \to B\) of \(\Fam(T)\) a family in \(T\), and we call its codomain \(B\) the base of the family.
A family \(u \in \Fam(T)\) is univalent if it is a \((-1)\)-truncated object of the category \(\Fam(T)\). We write
\[\Fam^{\univ}(T) \subseteq \Fam(T)\]
for the full subcategory spanned by the univalent families.