Higher Auslander’s defect and classifying substructures of \(\varvec{n}\)-exangulated categories

Abstract

Herschend–Liu–Nakaoka introduced the notion of an n-exangulated category. 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.