Classifying subcategories in quotients of exact categories

TL;DR

This paper provides a classification of specific subcategories within quotients of exact categories, focusing on triangulated and thick subcategories in algebraic triangulated categories derived from Frobenius categories.

Contribution

It offers a new classification framework for subcategories in quotients of exact categories, especially in algebraic triangulated categories from Frobenius categories.

Findings

Classified triangulated subcategories in algebraic triangulated categories.

Identified conditions for thick subcategories in stable categories.

Extended classification results to quotients of exact categories.

Abstract

We classify certain subcategories in quotients of exact categories. In particular, we classify the triangulated and thick subcategories of an algebraic triangulated category, i.e. the stable category of a Frobenius category.