Homology, Homotopy and Applications

Volume 5 (2003)

Number 1

Cubical abelian groups with connections are equivalent to chain complexes

Pages: 49 – 52

DOI: http://dx.doi.org/10.4310/HHA.2003.v5.n1.a2


Ronald Brown (Mathematics Division, School of Informatics, University of Wales, Bangor, Gwynedd, Wales, United Kingdom)

Philip J. Higgins (Department of Mathematical Sciences, Science Laboratories, Durham, United Kingdom)


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.


chain complexes, cubical sets with connections, abelian group objects, crossed complexes, globular and cubical $\omega$-categories

2010 Mathematics Subject Classification

18D35, 18G35, 55U15

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