Example 10.2.4.20. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $C_{\bullet }$ be a simplicial object of $\operatorname{\mathcal{C}}$. If the object $X = C_0$ admits a Čechnerve $\operatorname{\check{C}}_{\bullet }(X)$ (Definition 10.2.4.3), then the identity map $C_0 \rightarrow X$ can be promoted to a morphism of simplicial objects $C_{\bullet } \rightarrow \operatorname{\check{C}}_{\bullet }(X)$ (see Notation 10.2.4.4) which exhibits $\operatorname{\check{C}}_{\bullet }(X)$ as a $0$-coskeleton of $C_{\bullet }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$