The stable category of preordered groups

TL;DR

This paper introduces and analyzes the stable category of preordered groups linked to a Z-pretorsion theory, detailing its properties, kernels, cokernels, and universal property.

Contribution

It defines the stable category of preordered groups and explores its fundamental properties, kernels, cokernels, and universal characterization.

Findings

Description of Z-kernels and Z-cokernels in preordered groups

Establishment of the universal property of the stable category

Characterization of the stable category's properties

Abstract

In this article, we present the stable category of preordered groups associated with some Z-pretorsion theory. We first define such a category as well as the related functor, and then study their properties. By doing so, we provide a description of both Z-kernels and Z-cokernels in the category of preordered groups. Finally, we prove the universal property of the stable category.