Remark 3.1.5.15. Every $2$-morphism in the $2$-category $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ is invertible: that is, $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ is a $(2,1)$-category in the sense of Definition 2.2.8.5. Moreover, the homotopy category of $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ (in the sense of Construction 2.2.8.12) can be identified with the category $\mathrm{h} \mathit{\operatorname{Kan}}$ of Construction 3.1.5.10 (see Remark 2.4.6.18).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$