map reduces to the one of boundary through the construction of the cone of a chain map.

Chain homotopy

A chain homotopy offers a way to relate two chain maps that induce the same map on homology groups, even though the maps may be different. Given two chain complexes A and B, and two chain maps ''f'', ''g'' : ''A'' -> ''B'', a chain homotopy is a sequence of homomorphisms ''h''_''n'' : ''A''_''n'' -> ''B''_''n''+1 such that 1=''hd''_''A''

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