Admissible weak factorization systems on extriangulated categories

TL;DR

This paper introduces admissible weak factorization systems in extriangulated categories, establishing a bijection with cotorsion pairs and generalizing existing results in the context of these categories.

Contribution

It defines admissible weak factorization systems and links them to cotorsion pairs, extending known results to extriangulated categories.

Findings

Bijection between cotorsion pairs and admissible weak factorization systems

Equivalence between hereditary and compatible cotorsion pairs under certain conditions

Generalization of previous results by Di, Li, and Liang

Abstract

Extriangulated categories, introduced by Nakaoka and Palu, serve as a simultaneous generalization of exact and triangulated categories. In this paper, we first introduce the concept of admissible weak factorization systems and establish a bijection between cotorsion pairs and admissible weak factorization systems in extriangulated categories. Consequently, we give the equivalences between hereditary cotorsion pairs and compatible cotorsion pairs via admissible weak factorization systems under certain conditions in extriangulated categories, thereby generalizing a result by Di, Li, and Liang.