Corollary 4.6.7.25. 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.**
We will assume that $\operatorname{\mathcal{C}}$ has a final object $Y$; the case where $\operatorname{\mathcal{C}}$ has an initial object follows by a similar argument. Corollary 4.6.7.24 implies that the inclusion map $\{ Y\} \hookrightarrow \operatorname{\mathcal{C}}$ is right anodyne. In particular, it is anodyne and therefore a weak homotopy equivalence.
$\square$