English

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 nn-exact sequence theorem holds in any nn-abelian category. As an application, the nn-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

R2 v1 2026-06-23T14:01:57.951Z