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Quasi-equivalent vs. homotopy equivalent functors in $A_\infty$ categories

Suppose that $\mathcal{A}, \mathcal{B}$ are strictly unital $A_\infty$ categories, and $\mathcal{F}, \mathcal{G}: \mathcal{A} \rightarrow \mathcal{B}$ are (strictly unital) functors. On one hand, we ...