Derived equivalences of functor categories
type: Item
instance of: scholarly article
title: Derived equivalences of functor categories
zbMATH Open document ID: 1412.18013
author: Javad Asadollahi
author: Rasool Hafezi
author: Razieh Vahed
published in: Journal of Pure and Applied Algebra
publication date: 2018-11-09T00:00:00Z
full work available at URL: http://hdl.handle.net/21.11116/0000-0004-8903-E
review text: In the present paper the authors study equivalences between derived categories associated to functor categories. In this way they obtain natural generalizations of some classical results already known for derived categories of module categories. In the mai result of the paper (Theorem 3.14) it is proved that if $\mathcal{S}$ is a small pre-additive category and $\mathcal{T}$ is a set of perfect complexes in from $\mathrm{Mod}\text{-}\mathcal{S}$ then the derived category associated to $\mathrm{Mod}\text{-}\mathcal{T}$ is equivalent to the relative derived category of $\mathrm{Mod}\text{-}\mathcal{S}$ with respect to $\mathcal{T}$. Moreover, this equivalence induces by restrictions between important subcategories of these derived categories. In the last part of the paper there are presented many applications. These include equivalences of homotopy categories or Gorenstein derived equivalences associated to right coherent rings.
reviewed by: Simion Sorin Breaz
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16E35
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16G10
zbMATH DE Number: 6975791
zbMATH Keywords: functor category
zbMATH Keywords: derived category
zbMATH Keywords: derived equivalence
MaRDI profile type: Publication
OpenAlex ID: W2962895979
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DOI: 10.1016/J.JPAA.2018.05.015
description: scientific article; zbMATH DE number 6975791