Institute of Mathematics

Abstract:  For an integer $n\geq3$, 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.