Corollary 5.1.5.15. Let $\kappa $ be an uncountable regular cardinal and let $q: X \rightarrow S$ be a locally cartesian fibration of simplicial sets. Then $q$ is essentially $\kappa $-small if and only if, for every vertex $s \in S$, the $\infty $-category $X_{s} = \{ s\} \times _{S} X$ is essentially $\kappa $-small.
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