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Research Article | Open Access

From short exact sequences of abelian categories to short exact sequences of homotopy categories and derived categories

Yilin Wu( ), Guodong Zhou
Department of Mathematics, Shanghai Key laboratory of PMMP, East China Normal University, Shanghai 200241, China
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Abstract

We show that a short exact sequence of abelian categories gives rise to short exact sequences of abelian categories of complexes, homotopy categories and unbounded derived categories, refining a result of J. Miyachi.

Keywords

abelian categorieshomotopy categoriesunbounded derived categoriesshort exact sequencesrecollements

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Electronic Research Archive
Volume 30 Issue 2,
February 2022
Pages 535-564
DOI: 10.3934/era.2022028

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Cite this article:
Wu Y, Zhou G. From short exact sequences of abelian categories to short exact sequences of homotopy categories and derived categories. Electronic Research Archive, 2022, 30(2): 535-564. https://doi.org/10.3934/era.2022028

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Received: 29 November 2021
Revised: 19 January 2022
Accepted: 07 February 2022
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)