Kerodon

Definition 9.1.6.9. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa $ be a small infinite cardinal. We say that $\operatorname{\mathcal{C}}$ admits small $\kappa $-filtered colimits it admits $\operatorname{\mathcal{K}}$-indexed colimits, for every small $\kappa $-filtered $\infty $-category $\operatorname{\mathcal{K}}$. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves small $\kappa $-filtered colimits if it preserves $\operatorname{\mathcal{K}}$-indexed colimits, for every small $\kappa $-filtered $\infty $-category $\operatorname{\mathcal{K}}$.