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Proposition 9.2.1.23. Let $\kappa \leq \lambda < \mu $ be regular cardinals, where $\mu $ has exponential cofinality $\geq \lambda $. Then the functor

\[ \operatorname{Ind}_{\kappa }^{\lambda }: \operatorname{\mathcal{QC}}_{< \mu } \rightarrow \operatorname{\mathcal{QC}}_{< \mu } \]

is $(\lambda , \mu )$-finitary: that is, it commutes with $\mu $-small $\lambda $-filtered colimits.

Proof. By virtue of Remark 9.2.1.17, this is a special case of Corollary 9.1.10.11. $\square$