quasi-isomorphism

Let \(\mathcal{A}\) be an abelian category and \(\mathrm{Ch}(\mathcal{A})\) the category of chain complexes.

A chain map \(f_{*}: C_* \rightarrow D_*\) is said to be a quasi-isomorphism, if for each \(n \in \mathbb{N}\), the induced morphism by the chain homology functor

\begin{align*} H_n(f): H_n(C) \rightarrow H_n(D) \end{align*}

is an isomorphism