Example 8.1.7.7. Let $X$ be a Kan complex. Applying Proposition 8.1.7.6 (and noting that every edge of $X$ is an isomorphism), we see that $\rho _{+}: X \rightarrow \operatorname{Cospan}(X)$ is a homotopy equivalence of Kan complexes (see Corollary 8.1.3.11).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$