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Example (Objects of $\operatorname{\mathcal{S}}_{\ast }$). By definition, an object of the $\infty $-category $\operatorname{\mathcal{S}}_{\ast }$ is an edge $e: \Delta ^{0} \rightarrow X$ of the simplicial set $\operatorname{\mathcal{S}}= \operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{Kan})$ whose source is the Kan complex $\Delta ^{0}$. By virtue of Remark, this is the same data as a morphism $e: \Delta ^{0} \rightarrow X$ in the ordinary category of Kan complexes: that is, the data of a pointed Kan complex $(X,x)$ (Definition