Example 10.3.4.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $f: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{C}}$, and let $\operatorname{\mathcal{C}}^{0}_{/Y} \subseteq \operatorname{\mathcal{C}}_{/Y}$ be the sieve generated by $f$. If $f$ admits a right homotopy inverse $s: Y \rightarrow X$, then the sieve $\operatorname{\mathcal{C}}^{0}_{/Y}$ coincides with $\operatorname{\mathcal{C}}_{/Y}$, and is therefore dense. It follows that $f$ is a universal quotient morphism. In particular, every isomorphism is a universal quotient morphism.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$