N-extension closed subcategories of (n+2)-angulated categories

Abstract

Let $\mathcal{C}$ be a Krull-Schmidt $(n+2)$-angulated category and $\mathcal{A}$ be an $n$-extension closed subcategory of $\mathcal{C}$. Then $\mathcal{A}$ has the structure of an $n$-exangulated category in the sense of Herschend-Liu-Nakaoka. This construction gives $n$-exangulated categories which are not $n$-exact categories in the sense of Jasso nor $(n+2)$-angulated categories in the sense of Geiss-Keller-Oppermann in general. As an application, our result can lead to a recent main result of Klapproth.

8 pages. arXiv admin note: text overlap with arXiv:2108.07985, arXiv:2109.00196

References in corpus (1)

• $n$-Exact categories arising from $(n+2)$-angulated categories

Cited by in corpus (1)

• $n$-exact categories arising from $n$-exangulated categories