Kerodon

Variant 11.5.0.5. Let $\kappa \leq \lambda $ be regular cardinals. We say that $\operatorname{\mathcal{C}}$ admits $\lambda $-small $\kappa $-filtered colimits if it admits $\operatorname{\mathcal{K}}$-indexed colimits, for every $\infty $-category $\operatorname{\mathcal{K}}$ which is $\lambda $-small and $\kappa $-filtered. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves $\lambda $-small $\kappa $-filtered colimits if it preserves $\operatorname{\mathcal{K}}$-indexed colimits, for every $\infty $-category $\operatorname{\mathcal{K}}$ which is $\lambda $-small and $\kappa $-filtered.