From n-exangulated categories to n-abelian categories

Abstract

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 in the sense of Jasso and (n+2)-angulated in the sense of Geiss-Keller-Oppermann. Let C be an n-exangulated category with enough projectives and enough injectives, and X a cluster tilting subcategory of C. In this article, we show that the quotient category C/X is an n-abelian category, and it is equivalent to an n-cluster tilting subcategory of an abelian category with enough projectives. These results generalize the work of Jacobsen-Jørgensen and Zhou-Zhu for (n+2)-angulated categories. Moreover, it highlights new phenomena when it is applied to n-exact categories.