Lifting and restricting recollement data
type: Item
instance of: scholarly article
title: Lifting and restricting recollement data
zbMATH Open document ID: 1220.18011
author: Pedro Nicolás
author: Manuel Saorín
published in: Applied Categorical Structures
publication date: 2011-06-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/0804.1054
review text: The paper continues the authors' study of recollement data for triangulated categories with a generator [\textit{P. Nicolás} and \textit{M. Saorín}, J. Algebra 322, No.~4, 1220--1250 (2009; Zbl 1187.18008)]. In 1991, \textit{S.~König} gave a criterion for the bounded above derived category of a module category to be obtainable as a recollement. The present paper relates theorems of that type with unbounded analogues. The authors define the right bounded derived category \(D^-\mathcal A\) of a differential graded category \(\mathcal A\) to be the union of the aisles of the canonical t-structures of \(D\mathcal A\). They give a criterion for \(D^-\mathcal A\) to be a recollement of right bounded derived categories of the same type. They specialize this result to the case of dg-categories with cohomology concentrated in non-negative degrees, and also to the setting of König's theorem.
reviewed by: Wolfgang Rump
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 5909292
zbMATH Keywords: derived category
zbMATH Keywords: DG category
zbMATH Keywords: Morita theory
zbMATH Keywords: recollement
zbMATH Keywords: triangulated category
MaRDI profile type: Publication
OpenAlex ID: W2009118904
arXiv ID: 0804.1054
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DOI: 10.1007/S10485-009-9198-Z
description: scientific article