Example 2.2.8.28. Let $\operatorname{\mathcal{C}}$ be a category. Then the core $\operatorname{\mathcal{C}}^{\simeq } \subseteq \operatorname{\mathcal{C}}$ of Construction 1.3.5.4 coincides with the core $\operatorname{\mathcal{C}}^{\simeq } \subseteq \operatorname{\mathcal{C}}$ of Construction 2.2.8.27, where we regard $\operatorname{\mathcal{C}}$ as a $2$-category having only identity $2$-morphisms.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$