  Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It
is not only a higher dimensional analogue of extriangulated categories defined
by Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exact
categories and $(n+2)$-angulated categories. In this article, we give an
$n$-exangulated version of Auslander's defect and Auslander-Reiten duality
formula. Moreover, we also give a classification of substructures (=closed
subbifunctors) of a given skeletally small $n$-exangulated category by using
the category of defects.
