Proposition 8.7.3.2 (Functoriality of Cocompletion). Let $\mathbb {K}$ be a small collection of small simplicial sets. Then there exists a $\mathbb {K}$-cocompletion functor $T: \operatorname{\mathcal{QC}}\rightarrow \operatorname{\mathcal{QC}}$, which is uniquely determined up to isomorphism.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$