The generalized Auslander–Reiten duality on an exact category

DOI10.1142/S0219498818502274zbMath1407.16014arXiv1609.07732OpenAlexW3103867158MaRDI QIDQ4628698

Pengjie Jiao

Publication date: 15 March 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.07732

zbMATH Keywords

stable categoryAuslander-Reiten dualityalmost split conflationrepresentations of infinite quivers

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Abelian categories, Grothendieck categories (18E10)

Related Items (16)

The generalized auslander–reiten duality on a module category ⋮ Existence of n-Auslander–Reiten sequences via a finiteness condition ⋮ Classifications of exact structures and Cohen-Macaulay-finite algebras ⋮ Functors and morphisms determined by subcategories ⋮ Auslander's defect formula and a commutative triangle in an exact category ⋮ Almost split triangles and morphisms determined by objects in extriangulated categories ⋮ Auslander–Reiten–Serre duality for n-exangulated categories ⋮ Auslander–Reiten theory in extriangulated categories ⋮ Higher Auslander-Reiten sequences via morphisms determined by objects ⋮ Auslander-Reiten n -exangles and morphisms determined by objects in n -exangulated categories ⋮ The homotopy category of monomorphisms between projective modules ⋮ On the existence of Auslander-Reiten \((d+2)\)-angles in \((d+2)\)-angulated categories ⋮ A bijection triangle in extriangulated categories ⋮ Singular equivalences of functor categories via Auslander-Buchweitz approximations ⋮ Different exact structures on the monomorphism categories ⋮ The existence of n-Auslander–Reiten sequences via determined morphisms

Cites Work

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• Generalized Serre duality
• Covering spaces in representation-theory
• Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
• Chain complexes and stable categories
• Auslander-Reiten duality for Abelian categories.
• Almost split sequences and approximations
• Higher algebraic K-theory: I
• Representation theory of strongly locally finite quivers

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