Localization of extriangulated categories

In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with a natural, universal structure of an extriangulated category. This construction unifies the Serre quotient of abelian categories and the Verdier qu...

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Bibliographic Details
Published inJournal of algebra Vol. 611; pp. 341 - 398
Main Authors Nakaoka, Hiroyuki, Ogawa, Yasuaki, Sakai, Arashi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2022
Subjects
Exact categories
Extriangulated categories
Localizations
Triangulated categories
Triangulated categories
Exact categories
Localizations
Extriangulated categories
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Summary:In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with a natural, universal structure of an extriangulated category. This construction unifies the Serre quotient of abelian categories and the Verdier quotient of triangulated categories. Indeed we give such a construction for a bit wider class of morphisms, so that it covers several other localizations appeared in the literature, such as Rump's localization of exact categories by biresolving subcategories, localizations of extriangulated categories by means of Hovey twin cotorsion pairs, and the localization of exact categories by two-sided admissibly percolating subcategories.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.08.008