Example 9.3.3.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which contains a final object $Y$. Then every object $X \in \operatorname{\mathcal{C}}$ admits a morphism $f: X \rightarrow Y$ which is uniquely determined up to homotopy. In this case, the object $X$ is $n$-truncated (in the sense of Definition 9.3.1.1) if and only if the morphism $f$ is $n$-truncated (in the sense of Definition 9.3.3.1).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$