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:
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:
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.
Read more about this topic: Snake Lemma
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