On the Hereditariness of the Representations of Thread Quivers

Abstract

We prove a conjecture of Paquette, Rock, and Yildirim by showing that, for every thread quiver, the abelian category of pointwise finite dimensional representations is hereditary. Since this category typically lacks enough projectives and injectives, standard homological methods do not apply directly. Our approach combines a Yoneda Ext criterion for hereditariness, established in this paper, with structural reductions to the subcategory of quasi noise free representations. We also indicate an alternative proof using a Keller's theorem on derived categories.