Quasi-isomorphism

In homological algebra, a branch of mathematics, a quasi-isomorphism or quism is a morphism A → B of chain complexes such that the induced morphisms
of homology groups are isomorphisms for all n.
In the theory of model categories, quasi-isomorphisms are sometimes used as the class of weak [equivalence (homotopy theory)|weak equivalence]s when the objects of the category are chain or cochain complexes. This results in a homology-local theory, in the sense of Bousfield localization in homotopy theory.