The Hurewicz theorem for cubical homology

TL;DR

This paper provides an elementary proof of the Hurewicz theorem specifically for cubical Kan complexes, connecting homotopy and homology groups using loop space concepts.

Contribution

It introduces a new elementary proof of the Hurewicz theorem tailored for cubical Kan complexes, utilizing loop space notions from a companion paper.

Findings

Establishes the Hurewicz theorem for cubical Kan complexes

Develops an approach based on loop spaces of cubical sets

Bridges homotopy and homology in cubical contexts

Abstract

We give an elementary proof of the Hurewicz theorem relating homotopy and homology groups of a cubical Kan complex. Our approach is based on the notion of a loop space of a cubical set, developed in a companion paper ``Homotopy groups of cubical sets'' by the first two authors.