A note on singular equivalences
type: Item
instance of: scholarly article
title: A note on singular equivalences
zbMATH Open document ID: 1464.18014
DOI: 10.1134/S0001434621030354
author: Jian Feng
author: Dejun Wu
published in: Mathematical Notes
publication date: 2021-07-08T00:00:00Z
review text: For an exact sequence \(0\to \mathcal{A} \to \mathcal{B} \stackrel{e}{\to} \mathcal{C}\to 0\) of abelian categories such that \(\mathcal{B}\) and \(\mathcal{C}\) have enough projective objects, the authors give equivalent conditions for \(D^b_{\mathrm{sg}}(e): D^b_{\mathrm{sg}}(\mathcal{B}) \to D^b_{\mathrm{sg}}(\mathcal{C})\) inducing a singular equivalence. This generalizes the main theorem of \textit{X.-W. Chen} [Proc. Am. Math. Soc. 142, No. 8, 2633--2640 (2014; Zbl 1309.18010)].
reviewed by: Olaf Teschke
Mathematics Subject Classification ID: 18G80
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 7369742
zbMATH Keywords: exact sequence
zbMATH Keywords: singularity category
zbMATH Keywords: triangle equivalence
MaRDI profile type: Publication
cites work: Des catégories abéliennes
cites work: Q3409132
cites work: Singular equivalences induced by homological epimorphisms
cites work: Singular Equivalences of Trivial Extensions
cites work: Localization of triangulated categories and derived categories
full work available at URL: s0001434621030354
OpenAlex ID: W3178531688
description: scientific article; zbMATH DE number 7369742