# Kerodon

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Variant 8.3.5.7. Let $\kappa$ be an uncountable cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty$-category which is locally $\kappa$-small. Then, in the statement of Proposition 8.3.5.6, we can replace $\operatorname{\mathcal{S}}$ with the $\infty$-category $\operatorname{\mathcal{S}}^{< \kappa }$ of $\kappa$-small spaces (Variant 5.6.4.12).