Definition 4.7.5.1. Let $\kappa $ be an uncountable cardinal. We will say that a simplicial set $\operatorname{\mathcal{C}}$ is essentially $\kappa $-small if there exists a categorical equivalence of simplicial sets $\operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$, where $\operatorname{\mathcal{D}}$ is a $\kappa $-small $\infty $-category.
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