A note on model structures on arbitrary Frobenius categories

TL;DR

This paper establishes a model structure on any Frobenius category, ensuring its homotopy category aligns with the stable category as a triangulated category, thus connecting model category theory with Frobenius categories.

Contribution

It introduces a model structure on arbitrary Frobenius categories, linking their homotopy and stable categories in a triangulated framework.

Findings

Constructs a Quillen model structure on Frobenius categories.

Shows the homotopy category is equivalent to the stable category.

Provides a new perspective on Frobenius categories via model category theory.

Abstract

We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\F$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\F}$ as triangulated categories.