Remark 10.2.4.2. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $C_{\bullet }: \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})^{\operatorname{op}} \rightarrow \operatorname{\mathcal{C}}$ be a simplicial object of $\operatorname{\mathcal{C}}$. Then $X_{\bullet }$ is a Čechnerve if and only if it is right Kan extended from the full subcategory of $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})^{\operatorname{op}}$ spanned by the object $[0]$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$