Two talks based on my papers on exact categories.
Quillen’s exact category is a powerful framework for studying extension-closed subcategories of abelian categories, and provides many interesting questions on such subcategories. In the first talk, I will explain the basics of some properties and invariants of exact categories (e.g. the Jordan-Holder property, simple objects, and Grothendieck monoid). In the second talk, I will give some results and questions about particular classes of exact categories arising in the representation theory of algebras (e.g. torsion(-free) classes over path algebras and preprojective algebras). If time permits, I will discuss questions of whether these results can be generalized to extriangulated categories (extension-closed subcategories of triangulated categories).