Kerodon

Remark 4.5.1.27. Let $\operatorname {h}_{2} \mathit{\operatorname{Kan}}$ denote the homotopy bicategory of Kan complexes (Variant 3.1.6.9). Then $\operatorname {h}_{2} \mathit{\operatorname{Kan}}$ can be identified with the full subcategory of $\operatorname {h}_{2} \mathit{\operatorname{\mathbf{QCat}}}$ spanned by the Kan complexes. Since $\operatorname {h}_{2} \mathit{\operatorname{Kan}}$ is a $2$-category, this subcategory is contained in the pith $\operatorname {h}_{2} \mathit{\operatorname{QCat}} = \operatorname{Pith}( \operatorname {h}_{2} \mathit{\operatorname{\mathbf{QCat}}} )$; we can therefore also view $\operatorname {h}_{2} \mathit{\operatorname{Kan}}$ as a full subcategory of $\operatorname {h}_{2} \mathit{\operatorname{QCat}}$.