Kerodon

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Example 4.6.2.13. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between ordinary categories. Then $F$ is essentially surjective if and only if the induced map $\operatorname{N}_{\bullet }(F): \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ is an essentially surjective functor of $\infty$-categories (in the sense of Definition 4.6.2.9).