Kerodon

Remark 11.4.0.26. The definition of the pointed homotopy category $\mathrm{h} \mathit{\operatorname{Kan}}_{\ast }$ can be viewed as a special case of Construction 2.4.6.1, applied to the simplicial category $(\operatorname{Set}_{\Delta }^{\circ })_{\ast }$ of Construction 11.4.0.25. Invoking Proposition 2.4.6.9, we see that the category $\mathrm{h} \mathit{\operatorname{Kan}}_{\ast }$ of Construction 3.2.1.12 can be identified with the homotopy category of the $\infty $-category $\operatorname{\mathcal{S}}_{\ast }$ (as suggested by the notation).