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!