Definition 4.8.2.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n$ be an integer. We say that $\operatorname{\mathcal{C}}$ is locally $n$-truncated if, for every pair of objects $X,Y \in \operatorname{\mathcal{C}}$, the Kan complex $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ is $n$-truncated (see Definition 3.5.7.1).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$