The recollements induced by contravariantly finite subcategories
type: Item
instance of: scholarly article
title: The recollements induced by contravariantly finite subcategories
zbMATH Open document ID: 1487.18012
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2022-02-28T00:00:00Z
review text: The paper under review characterizes the existence of lower (upper) recollements of homotopy categories of bounded complexes in terms of the global dimension with respecto to a contravariantly (covariantly) finite subcategory \(\mathcal X\) of an abelian category (Theorems 3.11 and 3.12). Some applications of this characterization are provided in case \(\mathcal X\) is the class of Gorenstein projective modules over an \(n\)-Gorenstein ring (Corollary 3.3), or when \(\mathcal X\) is the class of FP-projective (FP-injective) modules (Corollaries 3.15 and 3.16). In the second part, the authors study the lifting of a recollement of a triple of abelian categories to a triple of relative derived categories with respect to balanced pairs. Applications include the case of Gorenstein derived categories (Corollary 5.8) and pure derived categories (Corollary 5.9).
reviewed by: S. Estrada
Mathematics Subject Classification ID: 18G80
Mathematics Subject Classification ID: 18G25
Mathematics Subject Classification ID: 18E35
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 13D05
zbMATH DE Number: 7481866
zbMATH Keywords: contravariantly finite subcategory
zbMATH Keywords: recollement
zbMATH Keywords: balanced pairs
author: Yong-Gang Hu
author: Hailou Yao
MaRDI profile type: Publication
full work available at URL: s12044-021-00649-0
OpenAlex ID: W4210346624
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DOI: 10.1007/S12044-021-00649-0
description: scientific article; zbMATH DE number 7481866