Corollary 9.4.8.15 (Limits of Accessible $\infty $-Categories). The $\infty $-category $\operatorname{\mathcal{QC}}^{\operatorname{Acc}}$ admits small limits, which are preserved by the inclusion functor $\iota : \operatorname{\mathcal{QC}}^{\operatorname{Acc}} \hookrightarrow \operatorname{\mathcal{QC}}_{\leq \Omega }$. Here $ \Omega $ denotes the strongly inaccessible cardinal of Remark 4.9.0.4.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. By virtue of Proposition 7.6.6.15 (together with Remarks 7.6.6.16 and Exercise 7.6.6.17), it will suffice to show that the $\infty $-category $\operatorname{\mathcal{QC}}^{\operatorname{Acc}}$ admits pullbacks and small products which are preserved by the inclusion functor $\iota $. For pullbacks this is a reformulation of Corollary 9.4.8.11 (see Example 7.6.3.4), and for small products it follows from Corollary 9.4.6.19 and Example 9.4.7.4. $\square$