  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 of one-sided $n$-suspended categories. We provide a general
framework for passing from one-sided $n$-suspended categories to one-sided
$n$-angulated categories. Besides, we give a method to construct $n$-angulated
quotient categories from Frobenius $n$-prile categories. These results
generalize their works by Jasso for $n$-exact categories, Lin for
$(n+2)$-angulated categories and Li for one-sided suspended categories.
