# Kerodon

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Remark 5.4.6.5 (Comparison with Pointed Spaces). Let us regard the $\infty$-category of spaces $\operatorname{\mathcal{S}}$ as a full subcategory of the $\infty$-category $\operatorname{\mathcal{QC}}$ (Remark 5.4.4.8). The inclusion $\operatorname{\mathcal{S}}\hookrightarrow \operatorname{\mathcal{QC}}$ determines a functor of coslice $\infty$-category $\operatorname{\mathcal{S}}_{\ast } \rightarrow \operatorname{\mathcal{QC}}_{\ast }$, This functor restricts to an isomorphism from $\operatorname{\mathcal{S}}_{\ast }$ with the full subcategory of $\operatorname{\mathcal{QC}}_{\ast }$ spanned by those pairs $(\operatorname{\mathcal{C}}, C)$, where $\operatorname{\mathcal{C}}$ is a Kan complex.