Kerodon

Remark 7.4.5.18. Let $\lambda $ be an uncountable cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is locally $\lambda $-small. Let $\kappa = \mathrm{ecf}(\lambda )$ be the exponential cofinality of $\lambda $ and let $K$ be a $\kappa $-small simplicial set. Then, in the statements of Proposition 7.4.5.16 and Corollary 7.4.5.17, we can replace $\operatorname{\mathcal{S}}$ by the $\infty $-category $\operatorname{\mathcal{S}}^{< \lambda }$ of $\lambda $-small spaces (see Variant 7.4.5.8).