Definition 9.4.5.1. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets. We say that $F$ is a Morita equivalence if, for every idempotent complete $\infty $-category $\operatorname{\mathcal{E}}$, precomposition with $F$ induces an equivalence of $\infty $-categories $\operatorname{Fun}( \operatorname{\mathcal{D}}, \operatorname{\mathcal{E}}) \rightarrow \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})$.
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