Quasi-isomorphism
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In homological algebra, a branch of mathematics, a quasi-isomorphism or quism is a morphism A → B of chain complexes (respectively, cochain complexes) such that the induced morphisms
- [math]\displaystyle{ H_n(A_\bullet) \to H_n(B_\bullet)\ (\text{respectively, } H^n(A^\bullet) \to H^n(B^\bullet)) }[/math]
of homology groups (respectively, of cohomology groups) are isomorphisms for all n.
In the theory of model categories, quasi-isomorphisms are sometimes used as the class of weak equivalences 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.
See also
References
- Gelfand, Sergei I., Manin, Yuri I. Methods of Homological Algebra, 2nd ed. Springer, 2000.
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