In this paper, we introduce the notion of a right semi-equivalence for right (n + 2)-angulated categories. Let \(\mathscr{C}\) be an n-exangulated category and \(\mathscr{X}\) be a strongly covariantly finite subcategory of \(\mathscr{C}\) . We prove that the right (n + 2)-angulated category \(\mathscr{C}/\mathscr{X}\) has an n-suspension functor that is a 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 n-suspension functor is a right semi-equivalence. Furthermore, we also prove that an n-exangulated category \(\mathscr{C}\) has the structure of a right (n + 2)-angulated category with a right semi-equivalence if and only if for any object \(X \in \mathscr{C}\) , the morphism X → 0 is a trivial inflation.
