Proposition 8.4.5.3. Let $\mathbb {K}$ be a collection of simplicial sets and let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then there exists an $\infty $-category $\widehat{\operatorname{\mathcal{C}}}$ and a functor $h: \operatorname{\mathcal{C}}\rightarrow \widehat{\operatorname{\mathcal{C}}}$ which exhibits $\widehat{\operatorname{\mathcal{C}}}$ as a $\mathbb {K}$-cocompletion of $\operatorname{\mathcal{C}}$. Moreover, the functor $h$ is dense and fully faithful.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$