Classifying dense (co)resolving subcategories of exact categories via Grothendieck groups

TL;DR

This paper develops a method to classify dense (co)resolving subcategories of exact categories using Grothendieck groups, extending ideas from triangulated categories to a broader context.

Contribution

It introduces a new classification framework for dense (co)resolving subcategories of exact categories through Grothendieck groups, generalizing Thomason's work on triangulated categories.

Findings

Established a correspondence between subcategories and Grothendieck groups.

Extended classification techniques from triangulated to exact categories.

Provided a new perspective on subcategory structure via algebraic invariants.

Abstract

Classification problems of subcategories have been deeply considered so far. In this paper, we discuss classifying dense (co)resolving subcategories of exact categories via their Grothendieck groups. This study is motivated by the classification of dense triangulated subcategories of triangulated categories due to Thomason.