Kerodon

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Corollary 9.2.3.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. If $\operatorname{\mathcal{C}}$ is equivalent to the nerve of an ordinary category, then $\operatorname{Ind}(\operatorname{\mathcal{C}})$ has the same property.

Proof. Apply Proposition 9.2.3.13 in the special case where $\kappa = \aleph _0$, $\lambda = \operatorname{\textnormal{\cjRL {t}}}$ (Example 9.2.1.9) and $n = 0$ (see Corollary 4.8.2.16). $\square$