General heart construction on a triangulated category. II: Associated homological functor

DOI10.1007/s10485-010-9226-zzbMath1264.18015arXiv0910.2539OpenAlexW2154382515MaRDI QIDQ453596

Hiroyuki Nakaoka, Noriyuki Abe

Publication date: 27 September 2012

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.2539

zbMATH Keywords

triangulated categoryheartt-structurecluster tilting subcategoryhomological functor

Mathematics Subject Classification ID

Related Items (11)

On rooted cluster morphisms and cluster structures in 2-Calabi-Yau triangulated categories ⋮ Abelian categories from triangulated categories via Nakaoka-Palu's localization ⋮ Hearts of twin cotorsion pairs on extriangulated categories ⋮ Almost split triangles and morphisms determined by objects in extriangulated categories ⋮ LOCALIZATIONS OF THE HEARTS OF COTORSION PAIRS ⋮ Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects ⋮ Phantom ideals and cotorsion pairs in extriangulated categories ⋮ Half exact functors associated with cotorsion pairs on exact categories ⋮ A simultaneous generalization of mutation and recollement of cotorsion pairs on a triangulated category ⋮ Equivalence of Hearts of Twin Cotorsion Pairs on Triangulated Categories ⋮ Auslander's defects over extriangulated categories: an application for the general heart construction

Cites Work

• Unnamed Item
• General heart construction on a triangulated category. I: Unifying \(t\)-structures and cluster tilting subcategories
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Homological and homotopical aspects of torsion theories

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