Remark 9.3.3.3. Let $f: X \rightarrow Y$ be a morphism in an $\infty $-category $\operatorname{\mathcal{C}}$. The condition that $f$ is $n$-truncated depends only on the homotopy class $[f]$, regarded as a morphism in the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$