Kerodon

Construction 5.5.3.1 (The $\infty $-Category of Pointed Spaces). Let $\operatorname{\mathcal{S}}= \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Kan})$ denote the $\infty $-category of spaces, and regard the Kan complex $\Delta ^0$ as an object of $\operatorname{\mathcal{S}}$. We let $\operatorname{\mathcal{S}}_{\ast }$ denote the coslice $\infty $-category $\operatorname{\mathcal{S}}_{ \Delta ^0 / }$. We will refer to $\operatorname{\mathcal{S}}_{\ast }$ as the $\infty $-category of pointed spaces.