Corollary 4.6.6.26. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which has either an initial object or a final object. Then $\operatorname{\mathcal{C}}$ is weakly contractible.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Let $Y$ be an final object of $\operatorname{\mathcal{C}}$. Then the inclusion $\{ Y\} \hookrightarrow \operatorname{\mathcal{C}}$ is right anodyne (Corollary 4.6.6.25), and therefore a weak homotopy equivalence. $\square$