Remark 7.4.4.7. In the situation of Theorem 7.4.4.6, condition $(1)$ does not depend on the cardinal $\kappa $. It follows that if a diagram $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{QC}}^{< \kappa }$ admits a limit in the $\infty $-category $\operatorname{\mathcal{QC}}^{< \kappa }$, then that limit is preserved by the inclusion functors $\operatorname{\mathcal{QC}}^{< \kappa } \hookrightarrow \operatorname{\mathcal{QC}}^{< \lambda }$ for $\lambda \geq \kappa $.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$