# Wide subcategories are semistable

## TL;DR

This paper proves that wide subcategories of module categories over finite dimensional algebras satisfying certain conditions are semistable under some stability, extending known bijections in representation theory.

## Contribution

It establishes that wide subcategories linked to two-term presilting complexes are semistable, broadening the understanding of stability conditions in algebra representations.

## Key findings

- Wide subcategories satisfying a finiteness condition are semistable.
- Wide subcategories associated with two-term presilting complexes are semistable.
- Provides a complement to Ingalls-Thomas-type bijections.

## 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.