Hereditary Categories with Serre Duality which are generated by Preprojectives

TL;DR

This paper proves that certain hereditary categories with Serre duality generated by preprojectives are derived equivalent to representations of specific quivers, linking abstract categorical properties to concrete quiver representations.

Contribution

It establishes a classification of hereditary categories with Serre duality generated by preprojectives via derived equivalence to thread quiver representations.

Findings

Hereditary categories with Serre duality generated by preprojectives are derived equivalent to thread quiver representations.

Provides a classification linking categorical properties to quiver representations.

Enhances understanding of the structure of hereditary categories with Serre duality.

Abstract

We show that every k-linear abelian Ext-finite hereditary category with Serre duality which is generated by preprojective objects is derived equivalent to the category of representations of a strongly locally finite thread quiver.