3. Wide Subcategories are Semistable

Abstract

For an arbitrary finite dimensional algebra $\Lambda$, we prove that any wide subcategory of $\Mod \Lambda$ satisfying a certain finiteness condition is $\theta$-semistable for some stability condition $\theta$. More generally, we show that wide subcategories of $\Mod \Lambda$ associated with two-term presilting complexes of $\Lambda$ are semistable. This provides a complement for Ingalls-Thomas-type bijections for finite dimensional algebras.