A bijection triangle in extriangulated categories

DOI10.1016/J.JALGEBRA.2020.12.043zbMath1459.18007OpenAlexW3127415399MaRDI QIDQ1998942

Lingling Tan, Ti Wei Zhao, Zhao Yong Huang

Publication date: 9 March 2021

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.12.043

zbMATH Keywords

Serre dualityextriangulated categoriesAuslander bijectionAuslander-Reiten-Serre dualityrestricted Auslander bijection

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Abelian categories, Grothendieck categories (18E10) Derived categories, triangulated categories (18G80)

Related Items (2)

Auslander–Reiten–Serre duality for n-exangulated categories ⋮ Morphisms determined by objects under Galois \(G\)-covering theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classifying substructures of extriangulated categories via Serre subcategories
• \(n\)-exangulated categories (I): definitions and fundamental properties
• The Auslander bijections and universal extensions
• Triangulated quotient categories revisited
• Phantom ideals and cotorsion pairs in extriangulated categories
• Stable equivalence of dualizing R-varieties
• Gorenstein injective and projective modules
• Smashing subcategories and the telescope conjecture -- an algebraic approach
• Relative homological algebra and purity in triangulated categories
• Grothendieck groups in extriangulated categories
• Auslander's defects over extriangulated categories: an application for the general heart construction
• Tilting subcategories in extriangulated categories
• Almost split triangles and morphisms determined by objects in extriangulated categories
• Abelian categories arising from cluster tilting subcategories
• A note on morphisms determined by objects
• Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories
• Proper classes and Gorensteinness in extriangulated categories
• Auslander-Reiten duality for Abelian categories.
• Hearts of twin cotorsion pairs on extriangulated categories
• The Category of Morphisms Between Projective Modules
• Representation theory of artin algebras iii almost split sequences
• Representation theory of artin algebras IV¹⁾Invariants given by almost split sequences
• The generalized Auslander–Reiten duality on an exact category
• Auslander–Reiten Triangles on Gorenstein Derived Categories
• Representation theory of strongly locally finite quivers
• Abelian categories arising from cluster tilting subcategories II: quotient functors
• Morphisms Determined by Objects in Triangulated Categories
• The Auslander bijections: how morphisms are determined by modules
• Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors

This page was built for publication: A bijection triangle in extriangulated categories