Encyclopedia > Chain complex

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Chain complex

In homological algebra, a chain complex is a sequence of abelian groups or modules A0, A1, A2... connected by homomorphisms dn : An -> An-1, such that the composition of any two consecutive maps is zero: dn o dn+1 = 0 for all n. Chain complexes are mainly used to define homology and cohomology.

Examples from topology, group theory...



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