Corollary 10.3.5.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits finite limits. Then $\operatorname{\mathcal{C}}$ is regular if and only if every morphism $f: X \rightarrow Y$ can be obtained by composing a universal quotient morphism $q: X \twoheadrightarrow Y_0$ with a monomorphism $i: Y_0 \hookrightarrow Y$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$