Homological algebra in \(n\)-abelian categories

DOI10.1007/s12044-017-0345-4zbMath1498.18013OpenAlexW2748890800MaRDI QIDQ1680371

Deren Luo

Publication date: 15 November 2017

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-017-0345-4

zbMATH Keywords

\(n\)-abelian category\(\mathsf {nExt}^*\)-correspondence\(n\)-Baer sum\(n\)-cluster tilting\(n\)-derived functor

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15)

Related Items (7)

\(n\)-exangulated categories (I): definitions and fundamental properties ⋮ Existence of n-Auslander–Reiten sequences via a finiteness condition ⋮ Localization theory in higher homological algebra ⋮ Representation of \(n\)-abelian categories in abelian categories ⋮ QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES ⋮ Transport of structure in higher homological algebra ⋮ The existence of n-Auslander–Reiten sequences via determined morphisms

Cites Work

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• \(n\)-abelian and \(n\)-exact categories
• Cluster tilting for higher Auslander algebras.
• Homological algebra in Abelian categories
• A note on homology in categories
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander correspondence.
• Yoneda extensions in Abelian categories
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Exact categories
• Exact Categories and Duality

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