  Herschend-Liu-Nakaoka introduced the concept of $n$-exangulated categories as
higher-dimensional analogues of extriangulated categories defined by
Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact
categories and $(n+2)$-angulated categories as specific examples. In this
article, we introduce the notion of hereditary $n$-exangulated categories,
which generalize hereditary extriangulated categories. We provide two classes
of hereditary $n$-exangulated categories through closed subfunctors.
Additionally, we define the concept of $0$-Auslander $n$-exangulated categories
and discuss the circumstances under which these two classes of hereditary
$n$-exangulated categories become $0$-Auslander.
