# Kerodon

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Remark 4.6.2.11. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between $\infty$-categories. Then $F$ is essentially surjective if and only if the induced functor of homotopy categories $f: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{\operatorname{\mathcal{D}}}$ is essentially surjective (in the sense of classical category theory).