# Torsion pairs and quasi-abelian categories

## TL;DR

This paper extends the concept of torsion pairs from abelian to quasi-abelian categories and generalizes algebraic Harder-Narasimhan filtrations within this broader context.

## Contribution

It introduces torsion pairs for quasi-abelian categories and provides characterizations, bridging concepts from abelian categories and applying to filtrations.

## Key findings

- Many torsion theoretic concepts translate to quasi-abelian categories
- Characterizations of torsion pairs in quasi-abelian categories
- Generalization of Harder-Narasimhan filtrations

## Abstract

We define torsion pairs for quasi-abelian categories and give several characterisations. We show that many of the torsion theoretic concepts translate from abelian categories to quasi-abelian categories. As an application, we generalise the recently defined algebraic Harder-Narasimhan filtrations to quasi-abelian categories.