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Cut cotorsion pairs. (English) Zbl 1497.18014

The authors introduce the concept of cotorsion pairs cut along subcategories of an abelian category. It is a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain subcategories. They also obtain some connections between cut cotorsion pairs and Auslander-Buchweitz approximation theory, by considering relative analogs for Frobenius pairs and Auslander-Buchweitz contexts. Finally they give some applications of main results.

MSC:

18G25 Relative homological algebra, projective classes (category-theoretic aspects)
18G10 Resolutions; derived functors (category-theoretic aspects)
18G20 Homological dimension (category-theoretic aspects)
18G35 Chain complexes (category-theoretic aspects), dg categories
18G80 Derived categories, triangulated categories
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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