Admissible weak factorization systems on extriangulated categories

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 on extriangulated categories. Consequently, some descriptions of hereditary cotorsion pairs and compatible cotorsion pairs are given via admissible weak factorization systems under certain conditions in extriangulated categories, thereby generalizing a result by Di, Li, and Liang.