Relative Oppermann-Thomas cluster tilting objects in \((n+2)\)-angulated categories

DOI10.1007/S10485-022-09673-1zbMath1498.18018OpenAlexW4214700597MaRDI QIDQ2674397

Zongyang Xie, Liu, Zhongkui, Xiao Yan Yang

Publication date: 12 September 2022

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10485-022-09673-1

zbMATH Keywords

cluster tilting objects\(n\)-abelian categoriessupport \(\tau_n\)-tilting pairs\((n+2)\)-angulated categories\(n\)-rigid objects

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10) Derived categories, triangulated categories (18G80)

Cites Work

• \(n\)-abelian and \(n\)-exact categories
• Maximal rigid subcategories in 2-Calabi-Yau triangulated categories.
• Cluster tilting for higher Auslander algebras.
• Higher-dimensional cluster combinatorics and representation theory
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander correspondence.
• \(n\)-abelian quotient categories
• \(d\)-abelian quotients of \((d+2)\)-angulated categories
• Tropical duality in \((d+2)\)-angulated categories
• Maximal \(\tau_d\)-rigid pairs
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Noetherian hereditary abelian categories satisfying Serre duality
• Relative cluster tilting objects in triangulated categories
• n-angulated categories
• Relative n-rigid objects in (n + 2)-angulated categories
• -tilting theory

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