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Let's $(K^{\bullet}, d^{\bullet})$ is the complex over field $A$ (i.e. all $K^{i}$ are vector spaces over this field) and $(L^{\bullet}, {\delta}^{\bullet})$ such that $$L^{i}=H^{i}(K)~\text{and all}~{\delta}^{i}=0.$$ Why this two complexes $K$ and $L$ are quasi-isomorphic? Why it's wrong for complex over ring?

Thanks a lot!

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