# Kerodon

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

Corollary 8.5.5.6 (Existence). Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. Then there exists a functor $H: \operatorname{\mathcal{C}}\rightarrow \widehat{\operatorname{\mathcal{C}}}$ which exhibits $\widehat{\operatorname{\mathcal{C}}}$ as an idempotent completion of $\operatorname{\mathcal{C}}$.