Cut cotorsion pairs

Abstract We present the concept of cotorsion pairs cut along subcategories an abelian category. This provides a generalization complete pairs, and represents general framework to find approximations restricted certain subcategories. also exhibit some connections between Auslander–Buchweitz approximation theory, by considering relative analogs for Frobenius contexts. Several applications are given in settings Gorenstein homological algebra, chain complexes, quasi-coherent sheaves, as well characterize important results on Finitistic Dimension Conjecture, existence right adjoints quotient functors Serre subcategories, description triangulated categories co- t -structures.