A new characterization of n-exangulated categories with (n+2)-angulated structure

Abstract

Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann and $n$-exact categories in the sense of Jasso. In this article, we show that an $n$-exangulated category has the structure of an $(n+2)$-angulated category if and only if for any object $X$ in the category, the morphism $0\to X$ is a trivial deflation and the morphism $X\to 0$ is a trivial inflation.

17 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2006.02223, arXiv:2007.01716, arXiv:1909.13284