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

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.11189
 Bibcode:
 2020arXiv200611189H
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Representation Theory;
 18G25 (18G10;
 18G20;
 18G35;
 18G80;
 16E65)
 EPrint:
 48 pages