Remark 9.4.5.6 (Isomorphism Invariance). Let $\operatorname{\mathcal{C}}$ be a simplicial set, let $\operatorname{\mathcal{D}}$ be an $\infty $-category, and suppose we are given a pair of diagrams $F,F': \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which are isomorphic (as objects of the $\infty $-category $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$). Then $F$ is a Morita equivalence if and only if $F'$ is a Morita equivalence.
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