From right (n+2)-angulated categories to n-exangulated categories

Abstract

The notion of right semi-equivalence in a right $(n+2)$-angulated category is defined in this article. Let $\mathcal{C}$ be an $n$-exangulated category and $\mathcal{X}$ is a strongly covariantly finite subcategory of $\mathcal{C}$. We prove that the standard right $(n+2)$-angulated category $\mathcal{C}/\mathcal{X}$ is right semi-equivalence under a natural assumption. As an application, we show that a right $(n+2)$-angulated category has an $n$-exangulated structure if and only if the suspension functor is right semi-equivalence. Besides, we also prove that an $n$-exangulated category $\mathcal{C}$ has the structure of a right $(n+2)$-angulated category with right semi-equivalence if and only if for any object $X\in \mathcal{C}$, the morphism $X\to 0$ is a trivial inflation.

12 pages. arXiv admin note: text overlap with arXiv:2006.02223

References in corpus (2)

• External triangulation of the homotopy category of exact quasi-category
• Right triangulated categories: As extriangulated categories, aisles and co-aisles