Why chain complexes? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-24T10:57:39Z http://mathoverflow.net/feeds/question/69797 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/69797/why-chain-complexes Why chain complexes? Ricky 2011-07-08T13:34:22Z 2011-07-08T13:34:22Z <blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/68339/motivating-the-category-of-chain-complexes" rel="nofollow">Motivating the category of chain complexes</a> </p> </blockquote> <p>Chain complexes (of, say, abelian groups) are fundamental in homological algebra and algebraic geometry. For example, using the derived category of an abelian category is very natural nowadays. From another point of view, a lot of people are working on generalizing this ideas to the non abelian world (using simplicial stuff), see for example <a href="http://mathoverflow.net/questions/58497/is-there-a-high-concept-explanation-for-why-simplicial-leads-to-homotopy-theor/58530#58530" rel="nofollow">this</a> answer.</p> <p>So my question is: why chain complexes? I already know that they are extremely useful, but I'm looking for some theoretical reason for study them.</p> <p>Ricky</p>