Exercise 8.1.6.11. Show that, if the conditions of Corollary 8.1.6.10 are satisfied, then the diagram $Y \xrightarrow {g} B \xleftarrow {f} X$ is a homotopy inverse of $e$, when regarded as a morphism from $Y$ to $X$ in the $(\infty ,2)$-category $\operatorname{Cospan}^{L,R}(\operatorname{\mathcal{C}})$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$