Example 6.2.2.18. Combining Example 6.2.2.6 with Proposition 6.2.2.13, we see that the inclusion functor $\operatorname{\mathcal{S}}\hookrightarrow \operatorname{\mathcal{QC}}$ admits both a right adjoint (given on objects by the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{\mathcal{C}}^{\simeq }$) and a left adjoint (given on objects by the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{Ex}^{\infty }(\operatorname{\mathcal{C}})$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$