Kerodon

Remark 2.2.8.30. Let $\operatorname{\mathcal{C}}$ be a $2$-category. Then the core $\operatorname{\mathcal{C}}^{\simeq }$ is a $2$-groupoid. This follows from Remark 2.2.8.25: it is immediate from the construction that $\operatorname{\mathcal{C}}^{\simeq }$ is a $(2,1)$-category, and the homotopy category $\mathrm{h} \mathit{(\operatorname{\mathcal{C}}^{\simeq })}$ is a groupoid by virtue of the isomorphism $\mathrm{h} \mathit{(\operatorname{\mathcal{C}}^{\simeq } )} \simeq \operatorname{hPith}(\operatorname{\mathcal{C}})^{\simeq }$ of Remark 2.2.8.29.