The Hurewicz model structure on simplicial $R$-modules

TL;DR

This paper explores the Hurewicz model structure on simplicial modules over a ring, describing their properties and showing they are monoidal, extending known model structures from chain complexes via Dold--Kan correspondence.

Contribution

It provides a detailed description of the Hurewicz model structure on simplicial modules and proves these categories are monoidal, extending existing model structures.

Findings

Both model categories are monoidal.

The Hurewicz model structure on simplicial modules is characterized.

The Dold--Kan correspondence induces a model structure on simplicial modules.

Abstract

By a theorem of Christensen and Hovey, the category of non-negatively graded chain complexes has a model structure, called the h-model structure or Hurewicz model structure, where the weak equivalences are the chain homotopy equivalences. The Dold--Kan correspondence induces a model structure on the category of simplicial modules. In this paper, we give a description of the two model categories and some of their properties, notably the fact that both are monoidal.