Homology, Homotopy and Applications

Cubical abelian groups with connections are equivalent to chain complexes

Abstract

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.

Article information

Source
Homology Homotopy Appl., Volume 5, Number 1 (2003), 49-52.

Dates
First available in Project Euclid: 13 February 2006

https://projecteuclid.org/euclid.hha/1139839925

Mathematical Reviews number (MathSciNet)
MR1989612

Zentralblatt MATH identifier
1025.18006

Subjects
Primary: 18D35: Structured objects in a category (group objects, etc.)
Secondary: 55U15: Chain complexes

Citation

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