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About: Horseshoe lemma     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Statement106722453, within Data Space : dbpedia.org associated with source document(s)

Type: yago:WikicatLemmasyago:Abstraction100002137yago:Communication100033020yago:Lemma106751833yago:Message106598915yago:Proposition106750804yago:Statement106722453 New Facet based on Instances of this Class

In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects and to resolutions ofextensions of by . It says that if an object is an extension of by , then a resolution of can be built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of and . The name of the lemma comes from the shape of the diagram illustrating the lemma's hypothesis.