From recollement of triangulated categories to recollement of abelian categories
type: Item
instance of: scholarly article
title: From recollement of triangulated categories to recollement of abelian categories
zbMATH Open document ID: 1206.18012
author: MinXiong Wang
author: Yanan Lin
published in: Science China. Mathematics
publication date: 2010-06-21T00:00:00Z
review text: The goal of the paper is to show that if a triangulated category \(\mathcal D\) admits a recollement with respect to the triangulated categories \(\mathcal D'\), \(\mathcal D''\) given by the maps \(i_*:\mathcal D'\to \mathcal D\), \(j^ *:\mathcal D\to \mathcal D''\), \(i^ *,i^ !:\mathcal D\to \mathcal D'\) and \(j_!,j_*:\mathcal D''\to \mathcal D\), then the induced abelian category \(\mathcal D/\mathcal T\) (where \(\mathcal T\) is a cluster tilting subcategory of \(\mathcal D\)) also admits a recollement relative to the abelian categories \(\mathcal D'/i^ *(\mathcal T)\) and \(\mathcal D''/j^ *(\mathcal T)\), provided that \(\mathcal T\) satisfies \(i_*i^ *(\mathcal T)\subset \mathcal T\), \(j_*j^*(\mathcal T)\subset \mathcal T\).
reviewed by: S. Estrada
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 5723660
zbMATH Keywords: triangulated category
zbMATH Keywords: abelian category
zbMATH Keywords: recollement
zbMATH Keywords: tilting subcategory
zbMATH Keywords: quotient category
MaRDI profile type: Publication
full work available at URL: s11425-009-0189-1
OpenAlex ID: W1996792582
cites work: Q3320507
cites work: Recollements of extension algebras
cites work: Recollements, idempotent completions and t-structures of triangulated categories
cites work: Algebraic stratification in representation categories
cites work: Q3804882
cites work: Comparison of abelian categories recollements
cites work: Q3994341
cites work: Q3125202
cites work: Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
cites work: From triangulated categories to abelian categories: cluster tilting in a general framework
cites work: One-point extension and recollement.
cites work: Elementary construction of perverse sheaves
cites work: Q4296949
DOI: 10.1007/S11425-009-0189-1
description: scientific article; zbMATH DE number 5723660