Kerodon

Remark 9.2.4.8. In the situation of Definition 9.2.4.7, any functor from $\operatorname{\mathcal{D}}$ to $\operatorname{\mathcal{S}}_{< \lambda }$ can also be regarded as a functor from $\operatorname{\mathcal{D}}$ to $\operatorname{\mathcal{S}}_{< \lambda '}$, for any $\lambda ' \geq \lambda $. In this case, replacing $\lambda $ by $\lambda '$ does not change the $\infty $-category of elements $\int _{\operatorname{\mathcal{D}}} \mathscr {F}$. Consequently, the condition that $\mathscr {F}$ is $\kappa $-flat does not depend on $\lambda $.