Remark 9.2.1.17. Let $\kappa \leq \lambda $ be regular cardinals, and let $\mathbb {K}$ be the collection of all $\lambda $-small $\kappa $-filtered $\infty $-categories. Then $T: \operatorname{\mathcal{QC}}_{< \mu } \rightarrow \operatorname{\mathcal{QC}}_{< \mu }$ is an $\operatorname{Ind}_{\kappa }^{\lambda }$-completion functor (in the sense of Definition 9.2.1.16) if and only if it is a $\mathbb {K}$-cocompletion functor (in the sense of Definition 8.7.3.3).
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