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Cubical abelian groups with connections are equivalent to chain complexes

Ronald Brown and Philip J. Higgins

The theorem of the title is deduced from the equivalence between crossed complexes and cubical $\omega$-groupoids with connections proved by the authors in 1981. In fact we prove the equivalence of five categories defined internally to an additive category with kernels.

Homology, Homotopy and Applications, Vol. 5(2003), No. 2, pp. 49-52

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