A commutative diagram of modules with exact rows yields an exact sequence from the kernels and cokernels of its three vertical maps. Applied degree by degree to a short exact sequence of chain complexes, it produces the connecting homomorphisms in the associated long exact homology sequence.
The Snake Lemma is a fundamental result in homological algebra, particularly in the study of abelian categories and exact sequences. It describes a way to construct a long exact sequence of homology groups from a commutative diagram involving two short exact sequences.
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