Corollary 10.2.5.21. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n \geq -1$ be an integer. Then an augmented (semi)simplicial object $C_{\bullet }$ of $\operatorname{\mathcal{C}}$ is $(n-1)$-coskeletal if and only if it is $n$-coskeletal and the face cube $\tau _{n}: \operatorname{\raise {0.1ex}{\square }}^{n+1} \rightarrow \operatorname{\mathcal{C}}$ is a limit diagram in $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$