# Kerodon

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Corollary 4.6.4.18. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $C \in \operatorname{\mathcal{C}}$ be an object. Then the slice and coslice diagonal maps

$\delta _{/C}: \operatorname{\mathcal{C}}_{/C} \hookrightarrow \operatorname{\mathcal{C}}\operatorname{\vec{\times }}_{\operatorname{\mathcal{C}}} \{ C\} \quad \quad \delta _{C/}: \operatorname{\mathcal{C}}_{C/} \hookrightarrow \{ C\} \operatorname{\vec{\times }}_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}$

are equivalences of $\infty$-categories.