# Kerodon

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Definition 4.5.1.10. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty$-categories. We will say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is an equivalence of $\infty$-categories if the homotopy class $[F]$ is an isomorphism in the homotopy category $\mathrm{h} \mathit{\operatorname{QCat}}$ of Construction 4.5.1.1. We say that $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ are equivalent if there exists an equivalence from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.