Homology, Homotopy and Applications
Volume 5 (2003)
Cubical abelian groups with connections are equivalent to chain complexes
Pages: 49 – 52
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