One-sided n-suspended categories

For an integer n ⩾ 3, we introduce a simultaneous generalization of (n − 2)-exact categories and n-angulated categories, referred to as one-sided n-suspended categories. Notably, one-sided n-angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their n-angulated counterparts. Additionally, we present a method for constructing n-angulated quotient categories from Frobenius n-prile categories. Our results unify and extend the previous work of Jasso on n-exact categories, Lin on (n + 2)-angulated categories, and Li on one-sided suspended categories.