Kerodon

Remark 2.4.6.18. Let $\operatorname{\mathcal{C}}_{\bullet }$ be a simplicial category. Then the homotopy category of $\operatorname{\mathcal{C}}_{\bullet }$ can be identified with the coarse homotopy category of the homotopy $2$-category $\mathrm{h}_{2} \mathit{\operatorname{\mathcal{C}}}$ of Construction 2.4.6.16, in the sense of Construction 2.2.8.2. That is, we have a canonical isomorphism $\mathrm{h} \mathit{\operatorname{\mathcal{C}}} \simeq \mathrm{h} \mathit{( \mathrm{h}_{2} \mathit{\operatorname{\mathcal{C}}} )}$.