Natural dualities between abelian categories
type: Item
instance of: scholarly article
title: Natural dualities between abelian categories
zbMATH Open document ID: 1245.18003
author: Flaviu Pop
published in: Central European Journal of Mathematics
publication date: 2012-01-16T00:00:00Z
review text: Let \(\mathcal A\) and \(\mathcal B\) be abelian categories. Let \(F: \mathcal A\rightarrow \mathcal B\) and \(G:\mathcal B\rightarrow \mathcal A\) be a pair of right adjoint contravariant functors with natural transformations of right adjunction \(\delta:1_\mathcal A\rightarrow GF\) and \(\zeta:1_\mathcal B\rightarrow FG\). If \(C\) is a class of \(\delta\)-reflexive objects of \(\mathcal A\), and \(n\) is a positive integer, it is proved that \(F\) and \(G\) induce a duality between the category of all objects of \(\mathcal A\) with a \(n\)-dominant left \(C\)-resolution and the category of \(\zeta\)-reflexive objects of \(\mathcal B\) with a \(n\)-dominant right \(F(C)\)-resolution.
reviewed by: Constantin Năstăsescu
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 5997995
zbMATH Keywords: contravariant functor
zbMATH Keywords: right adjoint functors
zbMATH Keywords: duality
zbMATH Keywords: dominant resolution
zbMATH Keywords: costar
zbMATH Keywords: generalized tilting module
MaRDI profile type: Publication
full work available at URL: s11533-011-0048-5
OpenAlex ID: W2119221488
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DOI: 10.2478/S11533-011-0048-5
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description: scientific article; zbMATH DE number 5997995