Remark 2.4.2.10. Let $\operatorname{\mathcal{C}}$ be an ordinary category, regarded as a strict $2$-category having only identity $2$-morphisms (Example 2.2.0.6). Then the simplicial category $\operatorname{\mathcal{C}}_{\bullet }$ associated to $\operatorname{\mathcal{C}}$ by Example 2.4.2.8 agrees with the simplicial category associated to $\operatorname{\mathcal{C}}$ by Example 2.4.2.4.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$