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Transferring $A_\infty$-structure from a module to its homology

Given an $A_\infty$-module $M$, which is a graded module $M=\bigoplus_{k\in\mathbb{Z}}M_k$ with morphisms $m_n^M\colon A^{\otimes(n-1)}\otimes M\rightarrow M$ of degree 2-n satisfying the $A_\infty$ ...
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