Kerodon

Remark 2.2.8.29. Let $\operatorname{\mathcal{C}}$ be a $2$-category. Then the inclusion functor $\operatorname{\mathcal{C}}^{\simeq } \hookrightarrow \operatorname{\mathcal{C}}$ is a functor of $2$-categories, which induces an isomorphism of categories from $\mathrm{h} \mathit{(\operatorname{\mathcal{C}}^{\simeq } )}$ to the core $\operatorname{hPith}(\operatorname{\mathcal{C}})^{\simeq }$ of the homotopy category $\operatorname{hPith}(\operatorname{\mathcal{C}})$.