From triangulated categories to abelian categories--cluster tilting in a general framework

2006/05/03 by Steffen Koenig, Bin Zhu, Koenig, Steffen +1 · 4 citations
Mathematics · #16G20 #16G70 #17B20 #19S99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0605100

openalex publication_date 2006/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We put cluster tilting in ageneral framework by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal one-orthogonal subcategory) carries an abelian structure. These abelian quotients turn out to be module categories of Goreisten algebras of dimension at most one.

Cited by

• Abelian quotients of categories of n-exangles
• Frieze patterns in representation theory
• From objects finitely presented by a rigid object in a triangulated category to 2-term complexes
• On tilting modules over cluster-tilted algebras

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