Rigid objects, triangulated subfactors and abelian localizations

DOI10.1007/s00209-012-1099-4zbMath1279.18010arXiv1305.2310OpenAlexW2964325047MaRDI QIDQ358845

Apostolos Beligiannis

Publication date: 9 August 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.2310

zbMATH Keywords

triangulated categoriesmutationslocalizationsstable categoriesCalabi-Yau categoriescalculus of fractionscluster-tilting objectsGorenstein categoriesrigid objects

Mathematics Subject Classification ID

Representations of associative Artinian rings (16G10) Abelian categories, Grothendieck categories (18E10) Relative homological algebra, projective classes (category-theoretic aspects) (18G25) Localization of categories, calculus of fractions (18E35) Cluster algebras (13F60)

Related Items

Relative stable categories and birationality, Abelian categories from triangulated categories via Nakaoka-Palu's localization, Relative cluster tilting objects in triangulated categories, Quotients of exact categories by pseudo-cluster-tilting subcategories, Pre-\((n + 2)\)-angulated categories, Ideal mutations in triangulated categories and generalized Auslander-Reiten theory, Relative rigid subcategories and \(\tau\)-tilting theory, Abelian hearts of twin cotorsion pairs, Abelian categories arising from cluster tilting subcategories, Hearts of twin cotorsion pairs revisited: integral and abelian hearts, Lifting to two-term relative maximal rigid subcategories in triangulated categories, NEARLY MORITA EQUIVALENCES AND RIGID OBJECTS, Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories, Relative homology, higher cluster-tilting theory and categorified Auslander-Iyama correspondence, A note on abelian quotient categories, Triangulated categories with cluster tilting subcategories, Quasi-abelian hearts of twin cotorsion pairs on triangulated categories

Cites Work

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• Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras.
• Relative homology, higher cluster-tilting theory and categorified Auslander-Iyama correspondence
• The stable Calabi-Yau dimension of tame symmetric algebras.
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• On the relation between cluster and classical tilting.
• The triangulated structure of the stable derived category
• Realizing maps between modules over Tate cohomology rings.
• Stable equivalence of dualizing R-varieties
• Equivalences of derived categories for symmetric algebras.
• Wakamatsu tilting modules.
• Relative homological algebra and purity in triangulated categories
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• On tilting modules over cluster-tilted algebras.
• Triangulated Categories
• Noetherian hereditary abelian categories satisfying Serre duality
• From triangulated categories to module categories via localization II: calculus of fractions
• Cluster structures for 2-Calabi–Yau categories and unipotent groups
• Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated Categories
• Cluster-tilted algebras
• On the structure of triangulated categories with finitely many indecomposables
• The Hall algebra of a spherical object
• Noncrossing partitions and representations of quivers
• The homological theory of contravariantly finite subcategories:auslander-buchweitz contexts, gorenstein categories and (co-)stabilization
• Quotients of cluster categories
• Homological and homotopical aspects of torsion theories
• On the Freyd categories of an additive category