Projectively generated d-abelian categories are d-cluster tilting

2016/08/29 by Sondre Kvamme, Kvamme, Sondre
Mathematics · #18E99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1608.07985

openalex publication_date 2016/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Building on work of Jasso, we prove that any projectively generated d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category with enough projectives. This supports the claim that d-abelian categories are good axiomatizations of d-cluster tilting subcategories.

Related

• Axiomatizing Subcategories of Abelian Categories
• From triangulated categories to abelian categories--cluster tilting in a general framework
• On the relation between cluster and classical tilting
• The completion of d-abelian categories
• nℤ-abelian and nℤ-exact categories