Corollary 8.5.4.27. 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 7.6.6.9 (with Remark 7.6.6.10 and Exercise 7.6.6.11), it will suffice to show that $\operatorname{\mathcal{QC}}'$ is closed under pullbacks and small products. The case of pullbacks follows from Corollary 8.5.4.25 (see Corollary 7.6.3.9), and the case of products follows from Remark 8.5.4.7 (see Example 7.6.1.17). $\square$