Remark 5.5.4.14. Let $\kappa $ and $\lambda $ be regular cardinals and suppose that $\kappa $ is less than or equal to the exponential cofinality $\mathrm{ecf}(\lambda )$ (see Definition 4.7.3.16). Then the $\infty $-category $\operatorname{\mathcal{QC}}^{< \kappa }$ is locally $\lambda $-small. This follows by combining Remarks 5.5.4.5 and 4.7.5.11. It follows that the full subcategory $\operatorname{\mathcal{S}}^{< \kappa } \subseteq \operatorname{\mathcal{QC}}^{< \kappa }$ is also locally $\lambda $-small.
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