Kerodon

Variant 9.4.8.15. Let $\{ F_ i: \operatorname{\mathcal{C}}_ i \rightarrow \operatorname{\mathcal{D}}_ i \} _{i \in I}$ be a small collection of accessible functors between accessible $\infty $-categories. Then there exists a small regular cardinal $\lambda $ such that each of the $\infty $-categories $\operatorname{\mathcal{C}}_{i}$ and $\operatorname{\mathcal{D}}_{i}$ is $\lambda $-accessible, and each of the functors $F_ i$ is $\lambda $-compact. Moreover, $\lambda $ can be chosen arbitrarily large.