The long $n$-exact sequence theorem in $n$-abelian categories
Representation Theory
2020-06-30 v2 Category Theory
Abstract
In this note, we show that the long -exact sequence theorem holds in any -abelian category. As an application, the -abelian version of Wakamatsu's Lemma is given.
Cite
@article{arxiv.2003.01493,
title = {The long $n$-exact sequence theorem in $n$-abelian categories},
author = {Deren Luo and Panyue Zhou},
journal= {arXiv preprint arXiv:2003.01493},
year = {2020}
}
Comments
Theorem 3.3 is not true in general. If it holds, for example, when n=2, we infer that all 2-cluster tilting subcategories are 2Z-cluster tilting, but it can't hold in general