Kerodon

Remark 4.5.1.27. Let $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ denote the homotopy $2$-category of Kan complexes (Construction 3.1.5.13). Then $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ can be identified with the full subcategory of $\mathrm{h}_{2} \mathit{\operatorname{\mathbf{QCat}}}$ spanned by the Kan complexes. Since $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ is a $(2,1)$-category, this subcategory is contained in the pith $\mathrm{h}_{2} \mathit{\operatorname{QCat}} = \operatorname{Pith}( \mathrm{h}_{2} \mathit{\operatorname{\mathbf{QCat}}} )$; we can therefore also view $\mathrm{h}_{2} \mathit{\operatorname{Kan}}$ as a full subcategory of $\mathrm{h}_{2} \mathit{\operatorname{QCat}}$.