Proposition 8.7.3.5. Let $\kappa < \lambda $ be infinite cardinals, where $\lambda $ is regular and exponential cofinality $\geq \kappa $, and let $\mathbb {K}$ be a collection of $\kappa $-small simplicial sets. Then there exists a $\mathbb {K}$-cocompletion functor $T: \operatorname{\mathcal{QC}}_{< \lambda } \rightarrow \operatorname{\mathcal{QC}}_{< \lambda }$, which is uniquely determined up to isomorphism.
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