  Let $\mathscr{C}$ be a Krull-Schmidt $n$-exangulated category and
$\mathscr{A}$ be an $n$-extension closed subcategory of $\mathscr{C}$. Then
$\mathscr{A}$ inherits the $n$-exangulated structure from the given
$n$-exangulated category in a natural way. This construction gives
$n$-exangulated categories which are not $n$-exact categories in the sense of
Jasso nor $(n+2)$-angulated categories in the sense of Geiss-Keller-Oppermann
in general. Furthermore, we also give a sufficient condition on when an
$n$-exangulated category $\mathscr{A}$ is an $n$-exact category. These results
generalize work by Klapproth and Zhou.
