Kerodon

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

Corollary 4.6.4.17. 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.