Cut notions in extriangulated categories related to Auslander–Buchweitz theory and cotorsion theory

In this work, we introduce cut notions for extriangulated categories related with Auslander–Buchweitz theory and cotorsion theory. Namely, cut [Formula: see text]-cotorsion pairs, cut Frobenius pairs and cut AB contexts. We show that there are correspondences that relate these cut notions. Finally, by using this, we characterize co-[Formula: see text]-structures in certain subcategories of triangulated categories.