Extriangulated factorization systems, $s$-torsion pairs and recollements

TL;DR

This paper introduces extriangulated factorization systems in extriangulated categories, establishing a bijection with s-torsion pairs and exploring their behavior under recollements, thereby advancing the structural understanding of these categories.

Contribution

It defines extriangulated factorization systems, proves a bijection with s-torsion pairs, and studies their gluing via recollements, extending the theory of extriangulated categories.

Findings

Established a bijection between s-torsion pairs and extriangulated factorization systems.

Analyzed the gluing of these systems under recollements.

Extended the structural framework of extriangulated categories.

Abstract

We introduce extriangulated factorization systems in extriangulated categories and show that there exists a bijection between $s$-torsion pairs and extriangulated factorization systems. We also consider the gluing of $s$-torsion pairs and extriangulated factorization systems under recollements of extriangulated categories.