Quasi-isomorphism is a concept that arises in the context of homological algebra and category theory, particularly in the study of chain complexes and their morphisms. In simple terms, a quasi-isomorphism is a morphism (map) between two chain complexes that induces isomorphisms on all levels of their homology.
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A chain map inducing isomorphisms on all homology groups. The same definition applies to a map of cochain complexes using cohomology groups. A quasi-isomorphism need not be an isomorphism in each degree.