Example 9.2.2.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. Then every identity morphism of $\operatorname{\mathcal{C}}$ is a transfinite composition of morphisms of $W$ (take $\alpha = 0$ in Definition 9.2.2.1). In particular, if $W$ is closed under transfinite composition, then it contains every identity morphism of $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$