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Proposition 9.5.4.12. The $\infty $-categories $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$ and $\operatorname{\mathcal{QC}}^{\operatorname{RPr}}$ admit small limits, which are preserved by the inclusion functors $\operatorname{\mathcal{QC}}^{\operatorname{LPr}} \hookrightarrow \operatorname{\mathcal{QC}}_{\leq \Omega } \hookleftarrow \operatorname{\mathcal{QC}}^{\operatorname{RPr}}$.

Proof. Combine Proposition 9.5.4.7 and Remark 9.5.4.9 (for the $\infty $-category $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$) with Variant 9.5.4.10 and Remark 9.5.4.11 (for the $\infty $-category $\operatorname{\mathcal{QC}}^{\operatorname{RPr}}$) $\square$