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.
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We thank the anonymous referee for a very thorough reading and numerous suggestions that helped improve the paper.
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Jiangsheng Hu was supported by the NSF of China (Grant Nos. 12171206 and 12126424), the Natural Science Foundation of Jiangsu Province (Grant No. BK20211358), Jiangsu 333 Project and Zhongwu Young Teachers Program for the Innovative Talents of Jiangsu University of Technology. Panyue Zhou was supported by the National Natural Science Foundation of China (Grant No. 11901190).
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Hu, J., Ma, Y., Zhang, D. et al. Higher Auslander’s defect and classifying substructures of \(\varvec{n}\)-exangulated categories. Appl Categor Struct 31, 15 (2023). https://doi.org/10.1007/s10485-023-09713-4
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DOI: https://doi.org/10.1007/s10485-023-09713-4