Wide subcategories are semistable

Abstract

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

8 pages

References in corpus (2)

• Stability conditions, $\tau$-tilting Theory and Maximal Green Sequences
• Semibricks

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