Corollary 10.2.3.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n \geq 0$ be an integer. Then a simplicial object $X_{\bullet }$ of $\operatorname{\mathcal{C}}$ is $(n-1)$-skeletal if and only if it is $n$-skeletal and the degeneracy cube $\sigma _{n}: \operatorname{\raise {0.1ex}{\square }}^{n} \rightarrow \operatorname{\mathcal{C}}$ is a colimit diagram in $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$