Corollary 4.8.2.19. Let $n \geq -1$ be an integer. Then the inclusion functor $\mathrm{h} \mathit{\operatorname{QCat}}^{\leq n} \hookrightarrow \mathrm{h} \mathit{\operatorname{QCat}}$ admits a left adjoint, given on objects by the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{cosk}_{n+1}(\operatorname{\mathcal{C}})$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$