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The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology. Homomorphisms constructed with its help are generally called ''connecting homomorphisms''. == Statement == In an abelian category (such as the category of abelian groups or the category of vector spaces over a given field), consider a commutative diagram: :File:Snake lemma origin.svg where the rows are exact sequences and 0 is the zero object. Then there is an exact sequence relating the kernels and cokernels of ''a'', ''b'', and ''c'': : where ''d'' is a homomorphism, known as the ''connecting homomorphism''. Furthermore, if the morphism ''f'' is a monomorphism, then so is the morphism, ker ''a'' → ker ''b'', and if ''g is an epimorphism, then so is coker ''b'' → coker ''c''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「snake lemma」の詳細全文を読む スポンサード リンク
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