Homology, Homotopy and Applications
- Homology Homotopy Appl.
- Volume 5, Number 1 (2003), 49-52.
Cubical abelian groups with connections are equivalent to chain complexes
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 Appl., Volume 5, Number 1 (2003), 49-52.
First available in Project Euclid: 13 February 2006
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18D35: Structured objects in a category (group objects, etc.)
Secondary: 55U15: Chain complexes
Brown, Ronald; Higgins, Philip J. Cubical abelian groups with connections are equivalent to chain complexes. Homology Homotopy Appl. 5 (2003), no. 1, 49--52. https://projecteuclid.org/euclid.hha/1139839925