The long $n$-exact sequence theorem in $n$-abelian categories

Abstract

In this note, we show that the long $n$-exact sequence theorem holds in any $n$-abelian category. As an application, the $n$-abelian version of Wakamatsu's Lemma is given.

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