Kerodon

Variant 7.6.2.19. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a left fibration of $\infty $-categories, and suppose that the fibers of $U$ are essentially $\kappa $-small for some uncountable cardinal $\kappa $. Then, in the statements of Proposition 7.6.2.17 and Corollary 7.6.2.18, we can replace $\operatorname{\mathcal{S}}$ by the $\infty $-category $\operatorname{\mathcal{S}}^{< \kappa }$ of $\kappa $-small spaces (see Variant 5.5.4.12).