Zig-Zag Lemma
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, particularly homological algebra, the zig-zag lemma asserts the existence of a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category. The maps alpha_ ^{ } and beta_ ^{ } are the usual maps induced by homology. The boundary maps delta_n^{ } are explained below. The name of the lemma arises from the "zig-zag" behavior of the maps in the sequence. In an unfortunate overlap in…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, particularly homological algebra, the zig-zag lemma asserts the existence of a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category. The maps alpha_ ^{ } and beta_ ^{ } are the usual maps induced by homology. The boundary maps delta_n^{ } are explained below. The name of the lemma arises from the "zig-zag" behavior of the maps in the sequence. In an unfortunate overlap in terminology, this theorem is also commonly known as the "snake lemma," although there is another result in homological algebra with that name. Interestingly, the "other" snake lemma can be used to prove the zig-zag lemma, in a manner different from what is described below.