Quasi-abelian hearts of twin cotorsion pairs on triangulated categories

DOI10.1016/j.jalgebra.2019.06.011zbMath1475.18022arXiv1807.05423OpenAlexW2883176399WikidataQ127656238 ScholiaQ127656238MaRDI QIDQ2312863

Amit Shah

Publication date: 18 July 2019

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

Full work available at URL: https://arxiv.org/abs/1807.05423

zbMATH Keywords

triangulated categorylocalisationheartcluster categoryquasi-abelian categorytwin cotorsion pair

Mathematics Subject Classification ID

Torsion theories, radicals (18E40) Preadditive, additive categories (18E05) Localization of categories, calculus of fractions (18E35) Derived categories, triangulated categories (18G80)

Related Items

Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories ⋮ Torsion pairs and quasi-abelian categories ⋮ Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• General heart construction for twin torsion pairs on triangulated categories
• Rigid objects, triangulated subfactors and abelian localizations
• General heart construction on a triangulated category. I: Unifying \(t\)-structures and cluster tilting subcategories
• Auslander-Reiten theory in a Krull-Schmidt category
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• Injective and flat covers, envelopes and resolvents
• Preprojective modules over Artin algebras
• Applications of contravariantly finite subcategories
• Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
• Hearts of twin cotorsion pairs on extriangulated categories
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Quiver representations.
• From triangulated categories to module categories via localisation
• From triangulated categories to module categories via localization II: calculus of fractions
• NEARLY MORITA EQUIVALENCES AND RIGID OBJECTS
• Cluster-tilted algebras
• Representation theory of artin algebras IV¹⁾Invariants given by almost split sequences
• Representation theory of artin algebras v: methods for computing aimost split sequences and irreducible morphisms
• Auslander-Reiten triangles in subcategories
• A counterexample to Raikov's conjecture
• A Torsion Theory for Abelian Categories
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

This page was built for publication: Quasi-abelian hearts of twin cotorsion pairs on triangulated categories