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