Localization theory in higher homological algebra

DOI10.1016/j.jalgebra.2023.07.035OpenAlexW4385491510MaRDI QIDQ6051009

Konstantinos Liampis

Publication date: 19 September 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2023.07.035

zbMATH Keywords

\(n\)-angulated categories\(n\)-abelian categories\(n\)-cluster tilting subcategoriesGabriel-Zisman localizations

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10) Preadditive, additive categories (18E05) Localization of categories, calculus of fractions (18E35) Derived categories, triangulated categories (18G80)

Cites Work

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• \(n\)-abelian and \(n\)-exact categories
• Relative homology, higher cluster-tilting theory and categorified Auslander-Iyama correspondence
• Idempotent completion of \(n\)-angulated categories
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander correspondence.
• Homological algebra in \(n\)-abelian categories
• Localization of extriangulated categories
• The Karoubi envelope and weak idempotent completion of an extriangulated category
• Representation of \(n\)-abelian categories in abelian categories
• Axiomatizing subcategories of abelian categories
• Right n-angulated categories arising from covariantly finite subcategories
• n-angulated categories
• Idempotent completion of triangulated categories

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