Example 7.6.6.8. Let $\lambda $ be an uncountable cardinal and let $\kappa = \mathrm{cf}(\lambda )$ denote its cofinality. Then the $\infty $-categories $\operatorname{\mathcal{S}}^{< \lambda }$ and $\operatorname{\mathcal{QC}}^{< \lambda }$ are $\kappa $-cocomplete. Moreover, the inclusion maps
\[ \operatorname{\mathcal{S}}^{ < \lambda } \hookrightarrow \operatorname{\mathcal{S}}\quad \quad \operatorname{\mathcal{QC}}^{< \lambda } \hookrightarrow \operatorname{\mathcal{QC}} \]
preserve $\kappa $-small colimits. See Corollaries 7.4.5.20 and 7.4.3.8. In particular, if $\kappa = \lambda $ is an uncountable regular cardinal, then the $\infty $-categories $\operatorname{\mathcal{S}}^{< \kappa }$ and $\operatorname{\mathcal{QC}}^{< \kappa }$ are $\kappa $-cocomplete.