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

Abstract

Let $\mathcal{C}$ be a Krull-Schmidt $n$-exangulated category and $\mathcal{A}$ be an $n$-extension closed subcategory of $\mathcal{C}$. Then $\mathcal{A}$ inherits the $n$-exangulated structure from the given $n$-exangulated category in a natural way. 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. Furthermore, we also give a sufficient condition on when an $n$-exangulated category $\mathcal{A}$ is an $n$-exact category. These results generalize work by Klapproth and Zhou.

16 pages. arXiv admin note: substantial text overlap with arXiv:2109.02068; text overlap with arXiv:2108.07985, arXiv:2109.00196

References in corpus (3)

• External triangulation of the homotopy category of exact quasi-category
• $n$-Exact categories arising from $(n+2)$-angulated categories
• N-extension closed subcategories of (n+2)-angulated categories

Cited by in corpus (2)

• Higher Auslander-Reiten sequences via morphisms determined by objects
• Auslander-Reiten-Serre duality for n-exangulated categories