Idempotent completion of certain $n$-exangulated categories

Abstract

It was shown recently that an $n$-extension closed subcategory $\mathcal{A}$ of a Krull-Schmidt $(n+2)$-angulated category has a natural structure of an $n$-exangulated category. In this article, we prove that its idempotent completion $\tilde{\mathcal{A}}$ admits an $n$-exangulated structure. It is not only a generalization of the main result of Lin, but also gives an $n$-exangulated category which is neither $n$-exact nor $(n+2)$-angulated in general.

11 pages. arXiv admin note: text overlap with arXiv:2206.09658. substantial text overlap with arXiv:2109.02068; text overlap with arXiv:2011.00729, arXiv:2109.12954, arXiv:2108.07985, arXiv:2006.02223