Variant 9.1.10.10. Let $\kappa $ be a regular cardinal and let $\mathbb {K}$ be a collection of $\kappa $-small simplicial sets. For every uncountable regular cardinal $\lambda \geq \kappa $, the $\infty $-category $\operatorname{\mathcal{QC}}^{\mathbb {K}-\mathrm{cocont}}_{< \lambda }$ of Notation 8.7.3.7 admits $\lambda $-small $\kappa $-filtered colimits, which are preserved by the inclusion functor $\operatorname{\mathcal{QC}}^{\mathbb {K}-\mathrm{cocont}}_{< \lambda } \hookrightarrow \operatorname{\mathcal{QC}}_{< \lambda }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$