Example 10.2.3.22 (0-Skeleta). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $X_{\bullet }$ be a simplicial object of $\operatorname{\mathcal{C}}$, and set $C = X_0$. Then the constant simplicial object $\underline{C}$ is an $n$-skeleton of $X_{\bullet }$. More precisely, the identity morphism $\operatorname{id}: C \xrightarrow {\sim } X_0$ admits an (essentially unique) extension to a morphism of simplicial objects $\underline{C} \rightarrow X_{\bullet }$ which exhibits $\underline{C}$ as a $0$-skeleton of $X_{\bullet }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$