One-sided Frobenius pairs in extriangulated categories

Let l be an extriangulated category with a proper class xi of E-triangles. We introduce the notions of left Frobenius pairs, left (n-)cotorsion pairs and left (weak) Auslander-Buchweitz contexts with respect to xi in l. 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-Perez-Santiago's results in abelian categories.