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Quasi-isomorphism : ウィキペディア英語版
Quasi-isomorphism
In homological algebra, a branch of mathematics, a quasi-isomorphism is a morphism ''A'' → ''B'' of chain complexes (respectively, cochain complexes) such that the induced morphisms
:H_n(A_\bullet) \to H_n(B_\bullet)\ (\text H^n(A^\bullet) \to H^n(B^\bullet))\
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.
==References==

*Gelfand, Manin. ''Methods of Homological Algebra'', 2nd ed. Springer, 2000.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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