The Auslander-Reiten formula on finitely presented functor categories

DOI10.1007/s40840-020-01030-6zbMath1467.16005OpenAlexW3092283481MaRDI QIDQ2045221

Shoutao Guo, Xiao Yan Yang

Publication date: 12 August 2021

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-020-01030-6

zbMATH Keywords

transposeAuslander-Reiten translationfinitely presented functorAuslander-Reiten formula

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Chain complexes (category-theoretic aspects), dg categories (18G35) Derived categories, triangulated categories (18G80)

Cites Work

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• Applications of the defect of a finitely presented functor
• The Auslander-Reiten formula for complexes of modules.
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander-Reiten theory on the homotopy category of projective modules.
• Derived recollements and generalised AR formulas
• Relative homological algebra
• Notes on several orthogonal classes of flat and \(FP\)-injective functors
• Adjoint Functors
• Representation theory of artin algebras iii almost split sequences
• Auslander-Reiten duality for Grothendieck abelian categories
• Duality and contravariant functors in the representation theory of artin algebras
• Stable module theory
• Bifunctors and Adjoint Pairs

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