A homotopy theory for enrichment in simplicial modules

TL;DR

This paper develops a new homotopy theory framework for categories enriched in simplicial modules and chain complexes, extending existing models to a broader algebraic context.

Contribution

It introduces a Quillen model structure on enriched categories over simplicial modules and chain complexes, generalizing Bergner's model structure to new algebraic settings.

Findings

Established a Quillen model structure for enriched categories in simplicial modules.

Extended the homotopy theory framework to non-negatively graded chain complexes.

Provided a transfer method from simplicial categories to enriched categories over modules.

Abstract

We put a Quillen model structure on the category of small categories enriched in simplicial $k$-modules and non-negatively graded chain complexes of $k$-modules, where $k$ is a commutative ring. The model structure is obtained by transfer from the model structure on simplicial categories due to J. Bergner.