Classifying Subcategories in Quotients of Exact Categories - Classifying Triangulated and Thick Triangulated Subcategories of an Algebraic Triangulated Category

Abstract

The goal of this thesis is to prove a one-to-one correspondence between (thick) triangulated subcategories of the stable category associated with a Frobenius category and certain subcategories of the Frobenius category. The result is also generalized in the setting of an exact category and a quotient category. This thesis starts with an introduction to exact categories, quotient categories, Frobenius categories and the stable category of a Frobenius category. After this, the main results are explained and proved. Finally, a few applications are given.