Warning 10.2.5.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $C_{\bullet }$ be an augmented simplicial object of $\operatorname{\mathcal{C}}$. It follow from Remark 10.2.5.15 that if $C_{-1}$ is a final object of $\operatorname{\mathcal{C}}$, then $C_{\bullet }$ is $n$-coskeletal if and only if its underlying simplicial object is $n$-coskeletal. Beware that neither implication holds in general if we do not assume that $C_{-1}$ is final.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$