Remark 4.5.1.9. The left adjoint $\mathrm{h} \mathit{\operatorname{QCat}} \rightarrow \mathrm{h} \mathit{\operatorname{Kan}}$ of Proposition 4.5.1.8 admits a category-theoretic interpretation: it carries an $\infty $-category $\operatorname{\mathcal{C}}$ to the localization $\operatorname{\mathcal{C}}[W^{-1}]$ obtained by formally inverting the collection $W$ of all morphisms in $\operatorname{\mathcal{C}}$ (see Proposition 6.3.1.20).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$