Remark 9.2.8.14. It follows from Corollary 9.2.8.10 that the $\infty $-category $\operatorname{\mathcal{QC}}$ is compactly generated. In particular, it can be regarded as an $\operatorname{Ind}$-completion of the full subcategory $\operatorname{\mathcal{QC}}_{< \aleph _0}$ of finitely dominated $\infty $-categories (see Corollary 9.2.6.10), which is an idempotent completion of the $\infty $-category $\operatorname{\mathcal{QC}}_{\mathrm{fin}}$ (Proposition 9.2.6.13).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$