Kerodon

Remark 9.2.1.11. Let $\kappa \leq \lambda $ be regular cardinals and let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Suppose that $\operatorname{\mathcal{C}}$ is locally $\mu $-small, for some uncountable cardinal $\mu $ of exponential cofinality $\geq \lambda $. Then $\operatorname{Ind}_{\kappa }^{\lambda }(\operatorname{\mathcal{C}})$ is also locally $\mu $-small (Proposition 8.7.3.11). In particular, if $\operatorname{\mathcal{C}}$ is a locally small $\infty $-category, then $\operatorname{Ind}(\operatorname{\mathcal{C}})$ is also locally small.