Projectively generated $d$-abelian categories are $d$-cluster tilting
Category Theory
2016-10-25 v3 Representation Theory
Abstract
Building on work of Jasso, we prove that any projectively generated -abelian category is equivalent to a -cluster tilting subcategory of an abelian category with enough projectives. This supports the claim that -abelian categories are good axiomatizations of -cluster tilting subcategories.
Cite
@article{arxiv.1608.07985,
title = {Projectively generated $d$-abelian categories are $d$-cluster tilting},
author = {Sondre Kvamme},
journal= {arXiv preprint arXiv:1608.07985},
year = {2016}
}
Comments
6 pages. The previous version of this note was incomplete due to a typo in the statement of Lemma 3.22 in https://arxiv.org/abs/1405.7805 . This note is not intended for publication