Kerodon

Remark 9.2.4.10 (Monotonicity). Let $\lambda $ be an uncountable cardinal and let $\mathscr {F}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{S}}_{< \lambda }$ be a functor of $\infty $-categories. If $\mathscr {F}$ is $\kappa $-flat (for some regular cardinal $\kappa $), then it is also $\kappa '$-flat for every regular cardinal $\kappa ' \leq \kappa $ (see Remark 9.1.1.9). In particular, every $\kappa $-flat functor $\mathscr {F}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{S}}_{< \lambda }$ is flat.