Kerodon

Remark 5.5.5.6 (Comparison with Kan Complexes). Since every Kan complex is an $\infty $-category (Example 1.4.0.3), we can identify the simplicial category $\operatorname{Kan}$ of Construction 5.5.1.1 with a full simplicial subcategory of $\operatorname{\mathbf{QCat}}$. Passing to homotopy coherent nerves, we can identify $\infty $-category of spaces $\operatorname{\mathcal{S}}= \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Kan})$ with the full subcategory of $\operatorname{ \pmb {\mathcal{QC}} }= \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{\mathbf{QCat}})$ spanned by the Kan complexes.