2021/08/12 by Tan, Lingling, Gao, Yuqiong, Chen, Qinghua
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.05856
Let \mathscrC be an extriangulated category with a proper class ξ of 𝔼-triangles. We introduce the notions of left Frobenius pairs, left (n-)cotorsion pairs and left (weak) Auslander-Buchweitz contexts with respect to ξ in \mathscrC. We show how to construct left cotorsion pais from left n-cotorsion pairs, and establish a one-to-one correspondence between left Frobenius pairs and left (weak) Auslander-Buchweitz contexts. We also study the relation between a certain class of cotorsion pairs and that of n-cotorsion pairs. These work generalize Ma-Zhao-Huang's results in triangulated categories and partially generalize Becerril-Mendoza-Pérez-Santiago's results in abelian categories.