Corollary 8.5.4.28. Let $\operatorname{\mathcal{QC}}'$ be the full subcategory of $\operatorname{\mathcal{QC}}$ spanned by the (small) idempotent-complete $\infty $-categories. Then $\operatorname{\mathcal{QC}}'$ is closed under small limits in $\operatorname{\mathcal{QC}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. By virtue of Proposition 7.6.6.15 (with Remark 7.6.6.16 and Exercise 7.6.6.17), it will suffice to show that $\operatorname{\mathcal{QC}}'$ is closed under pullbacks and small products. The case of pullbacks follows from Corollary 8.5.4.26 (see Corollary 7.6.3.9), and the case of products follows from Remark 8.5.4.8 (see Example 7.6.1.20). $\square$