Example 3.2.4.2. Let $\operatorname{\mathcal{C}}$ be a category. If $\operatorname{\mathcal{C}}$ has an initial object or a final object, then the simplicial set $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is contractible (this is a special case of Proposition 3.1.6.9). In particular, for every integer $n \geq 0$, the standard simplex $\Delta ^ n$ is contractible.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$