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 $\mathscr C$ be an $n$-exangulated category and $\mathscr X$ is a strongly covariantly finite subcategory of $\mathscr C$. We prove that the standard right $(n+2)$-angulated category $\mathscr C/\mathscr X$ 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 $\mathscr C$ has the structure of a right $(n+2)$-angulated category with right semi-equivalence if and only if for any object $X\in\mathscr C$, the morphism $X\to 0$ is a trivial inflation.