The five lemma is a fundamental result in homological algebra that provides a criterion for the isomorphism of certain morphisms in a diagram of chain complexes. It states that if you have a commutative diagram with exact rows and two columns of chain complexes, then the morphisms between the two complexes can be deduced from the morphisms at the other levels if certain conditions are met. This result is crucial for establishing relationships between homology groups and understanding derived functors in abelian categories.
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