Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 3.2.1.12. 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 3.2.1.11. Invoking Proposition 2.4.6.8, we see that the category $\mathrm{h} \mathit{\operatorname{Kan}}_{\ast }$ of Construction 3.2.1.10 can be identified with the homotopy category of the $\infty $-category $\operatorname{Kan}_{\ast }$ (as suggested by the notation).