https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=128.111.193.4formulasearchengine - User contributions [en]2026-07-15T04:38:27ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Van_Hove_singularity&diff=12397Van Hove singularity2013-05-02T19:12:36Z<p>128.111.193.4: /* Experimental observation */</p>
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<div>In [[homological algebra]], a branch of [[mathematics]], a '''quasi-isomorphism''' is a morphism ''A'' → ''B'' of [[chain complex]]es (respectively, cochain complexes) such that the induced morphisms <br />
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:<math>H_n(A_\bullet) \to H_n(B_\bullet)\ (\text{respectively, } H^n(A^\bullet) \to H^n(B^\bullet))\ </math><br />
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of [[homology (mathematics)|homology]] groups (respectively, of cohomology groups) are isomorphisms for all ''n''.<br />
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In the theory of [[model category|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]].<br />
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==References==<br />
*Gelfand, Manin. ''Methods of Homological Algebra'', 2nd ed. Springer, 2000.<br />
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[[Category:Algebraic topology]]<br />
[[Category:Homological algebra]]</div>128.111.193.4