Kerodon

Remark 2.4.6.17. Let $\operatorname{\mathcal{C}}_{\bullet }$ be a simplicial category and let $\mathrm{h}_{2} \mathit{\operatorname{\mathcal{C}}}$ denote the homotopy $2$-category of $\operatorname{\mathcal{C}}$. Then the underlying category $\operatorname{\mathcal{C}}_0$ of $\operatorname{\mathcal{C}}_{\bullet }$ (in the sense of Example 2.4.1.4) coincides with the underlying category of the strict $2$-category $\mathrm{h}_{2} \mathit{\operatorname{\mathcal{C}}}$ (in the sense of Remark 2.2.0.3).