# Stratifying systems through $\tau$-tilting theory

## TL;DR

This paper explores the connection between $ au$-rigid modules and stratifying systems, demonstrating that each $ au$-rigid module induces a stratifying system that can be viewed as a signed $ au$-exceptional sequence, advancing the understanding of module category structures.

## Contribution

It establishes a new link between $ au$-rigid modules and stratifying systems, showing that every non-zero $ au$-rigid module induces a stratifying system that corresponds to a signed $ au$-exceptional sequence.

## Key findings

- Every non-zero $ au$-rigid module induces a stratifying system.
- Stratifying systems can be viewed as signed $ au$-exceptional sequences.
- Provides a new perspective on module category structures.

## Abstract

In this paper we first show that every non-zero $\tau$-rigid $A$-module induces at least one stratifying system in the module category of $A$. Moreover, we show that each of these stratifying systems can be seen as a signed $\tau$-exceptional sequence.