Precovers, localizations and stable homotopy

TL;DR

This paper introduces a new localization theorem for stable model categories, enabling explicit realization of Bousfield localization functors in the context of relative homological algebra for group algebras.

Contribution

It establishes a localization theorem for stable model categories generated by precovering classes, with applications to Bousfield localization in homological algebra.

Findings

Proves a new localization theorem for stable model categories.

Provides explicit constructions of Bousfield localization functors.

Applies results to relative homological algebra for group algebras.

Abstract

We prove a new localization theorem for stable model categories if the localizing subcategory is generated by a precovering class in the model category. We use this to show how one may explicitly realize certain Bousfield localization functors that arise naturally in the study of relative homological algebra for group algebras.