Kerodon

Remark 9.1.1.9. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa $ be a singular cardinal. Then $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if and only if it is $\kappa '$-filtered, for every infinite cardinal $\kappa ' < \kappa $. We will soon see that this is also equivalent to the requirement that $\operatorname{\mathcal{C}}$ is $\kappa ^{+}$-filtered (Corollary 9.1.5.9). Consequently, there is generally no harm in restricting Variant 9.1.1.4 to the special case where $\kappa $ is regular.