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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 $Xinmathscr C$, the morphism $Xto 0$ is a trivial inflation.
Let $mathscr{F}$ be an $(n+2)$-angulated Krull-Schmidt category and $mathscr{A} subset mathscr{F}$ an $n$-extension closed, additive and full subcategory with $operatorname{Hom}_{mathscr{F}}(Sigma_n mathscr{A}, mathscr{A}) = 0$. Then $mathscr{A}$ nat
Let $mathscr C$ be a Krull-Schmidt $(n+2)$-angulated category and $mathscr A$ be an $n$-extension closed subcategory of $mathscr C$. Then $mathscr A$ has the structure of an $n$-exangulated category in the sense of Herschend-Liu-Nakaoka. This constru
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 $n$-exact categories and $(n
Let $n$ be an integer greater or equal than $3$. We give a simultaneous generalization of $(n-2)$-exact categories and $n$-angulated categories, and we call it one-sided $n$-suspended categories. One-sided $n$-angulated categories are also examples o
In this paper we complete a chain of explicit Quillen equivalences between the model category for $Theta_{n+1}$-spaces and the model category of small categories enriched in $Theta_n$-spaces. The Quillen equivalences given here connect Segal category