Example 4.7.8.2. Let $\kappa $ be an uncountable cardinal and let $\operatorname{\mathcal{C}}$ be a category. Then the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is locally $\kappa $-small if and only if, for every pair of objects $X,Y \in \operatorname{\mathcal{C}}$, the set $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ is $\kappa $-small.
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