Corollary 10.2.6.15. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{C}}$ which admits a Čechnerve $\operatorname{\check{C}}_{\bullet }(X/Y)$. If $f$ admits a right homotopy inverse, then $\operatorname{\check{C}}_{\bullet }(X/Y)$ is a colimit diagram: that is, it exhibits $Y$ as a geometric realization of its underlying simplicial object.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$