Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example 6.2.2.12. Combining Example 6.2.2.6 with Proposition 6.2.2.7, 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 $\operatorname{\mathcal{C}}\mapsto \operatorname{Ex}^{\infty }(\operatorname{\mathcal{C}})$).