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Cut cotorsion pairs

Part of: Homological algebra Homological methods

Published online by Cambridge University Press:  10 December 2021

Mindy Huerta Open the ORCID record for Mindy Huerta [Opens in a new window] ,
Octavio Mendoza Open the ORCID record for Octavio Mendoza [Opens in a new window]  and
Marco A. Pérez Open the ORCID record for Marco A. Pérez [Opens in a new window]
Mindy Huerta*
Affiliation:
Instituto de Matemáticas. Universidad Nacional Autónoma de México. Circuito Exterior, Ciudad Universitaria. CP04510. Mexico City, MEXICO Instituto de Matemática y EstadÍstica “Prof. Ing. Rafael Laguardia”. Facultad de Ingeniería. Universidad de la República. CP11300. Montevideo, URUGUAY
Octavio Mendoza
Affiliation:
Instituto de Matemáticas. Universidad Nacional Autónoma de México. Circuito Exterior, Ciudad Universitaria. CP04510. Mexico City, MEXICO
Marco A. Pérez
Affiliation:
Instituto de Matemática y EstadÍstica “Prof. Ing. Rafael Laguardia”. Facultad de Ingeniería. Universidad de la República. CP11300. Montevideo, URUGUAY
*
Corresponding author Mindy Huerta. E-mail: mindy@matem.unam.mx
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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 Auslander–Buchweitz approximation theory, by considering relative analogs for Frobenius pairs and Auslander–Buchweitz contexts. Several applications are given in the settings of relative Gorenstein homological algebra, chain complexes, and quasi-coherent sheaves, as well as 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.

Keywords

cut cotorsion pairscut frobenius pairscut Auslander-Buchweitz contexts

MSC classification

Primary: 18G25: Relative homological algebra, projective classes
Secondary: 18G10: Resolutions; derived functors 18G20: Homological dimension 18G35: Chain complexes 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 3 , September 2022 , pp. 548 - 585
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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