Axiomatizing subcategories of Abelian categories

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Kvamme, Sondre¹ 

[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

关键词: Cluster tilting;    Abelian category;    Homological algebra;   

DOI  :  10.1016/j.jpaa.2021.106862

来源: Elsevier

【 摘 要 】

We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

【 授权许可】

Free