Cubical abelian groups with connections are equivalent to chain complexes

2002/12/11 by Brown, R., Higgins, Philip J. · 1 citation
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0212157

Abstract

The theorem of the title is deduced from the equivalence between crossed complexes and cubical ω-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.

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• Enriched model categories and the Dold-Kan correspondence

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