Higher-dimensional Auslander–Reiten theory on (d+2)-angulated categories

DOI10.1017/S0017089521000343zbMath1494.18010arXiv1910.01454OpenAlexW3210320732MaRDI QIDQ5095568

Panyue Zhou

Publication date: 10 August 2022

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.01454

zbMATH Keywords

triangulated categoriesSerre functor\((d+2)\)-angulated categoriesAuslander-Reiten \((d+2)\)-angles

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Derived categories, triangulated categories (18G80)

Related Items

Auslander–Reiten–Serre duality for n-exangulated categories ⋮ Pre-\((n + 2)\)-angulated categories ⋮ Higher Auslander's defect and classifying substructures of \(n\)-exangulated categories

Cites Work

• \(n\)-abelian and \(n\)-exact categories
• The axioms for \(n\)-angulated categories
• The Grothendieck group of an \(n\)-angulated category
• Higher-dimensional cluster combinatorics and representation theory
• Auslander-Reiten \((d + 2)\)-angles in subcategories and a \((d + 2)\)-angulated generalisation of a theorem by Brüning
• Graded Calabi Yau algebras of dimension 3.
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Noetherian hereditary abelian categories satisfying Serre duality
• Right n-angulated categories arising from covariantly finite subcategories
• n-angulated quotient categories induced by mutation pairs
• REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS
• Representation theory of artin algebras IV¹⁾Invariants given by almost split sequences
• n-angulated categories
• Quotients of cluster categories
• The morphism axiom for n-angulated categories

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