On the extension-closed property for the subcategory $\text{Tr}({\Omega }^2(\mathrm{mod}-A))$

Abstract

We present a monomial quiver algebra $A$ having the property that the subcategory $\text{Tr}({\Omega }^2(\mathrm{mod}-A))$ is not extension-closed. This answers a question raised by Idun Reiten.