Two new classes of n-exangulated categories

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. Let C be an n-exangulated category and X a full subcategory of C. If X satisfies X subset of P boolean AND J, then we give a necessary and sufficient condition for the ideal quotient C / X to be an n-exangulated category, where P (resp. J) is the full subcategory of projective (resp. injective) objects in In addition, we define the notion of n-proper class in C. If xi is an n-proper class in C, then we prove that C admits a new n-exangulated structure. These two ways give n-exangulated categories which are neither n-exact nor (n + 2)-angulated in general. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

The notion of n-exangulated categories is introduced as both a higher dimensional analogue of extriangulated categories and a simultaneous generalization of n-exact categories and (n+2)-angulated categories. The necessary and sufficient condition for the ideal quotient C/X to be an n-exangulated category is provided, along with the definition of n-proper class in C. These two ways offer new n-exangulated categories that are neither n-exact nor (n+2)-angulated in general.