# Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory

## TL;DR

This paper introduces a new framework for understanding Gorenstein objects via homotopy categories of totally acyclic complexes, linking flat-cotorsion theory with Gorenstein homological algebra over coherent rings.

## Contribution

It defines a notion of total acyclicity for subcategories in abelian categories and applies it to describe cotorsion Gorenstein flat modules in a new, unified way.

## Key findings

- Gorenstein objects form a Frobenius category
- Stable category is equivalent to homotopy category of totally acyclic complexes
- Provides a new perspective on flat-cotorsion theory

## Abstract

We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to the homotopy category of totally acyclic complexes. Applied to the flat-cotorsion theory over a coherent ring, this provides a new description of the category of cotorsion Gorenstein flat modules; one that puts it on equal footing with the category of Gorenstein projective modules.