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From n-exangulated categories to n-abelian categories
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.jalgebra.2021.03.029
Yu Liu , Panyue Zhou

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.



中文翻译:

n个扩展类别到n个阿贝尔类别

Herschend-Liu-Nakaoka引入了n扩展类别的概念。它不仅是由Nakaoka-Palu定义的无穷大类别的高维类似物,而且在Jasso和Jasso的意义上给出了n个精确大类的同时推广。ñ+2个-在Geiss-Keller-Oppermann的意义上成角度。让C成为n扩展类别,具有足够的射影和足够的内射词,并且X 的集群倾斜子类别 C。在本文中,我们显示了商类别C/XÑ -abelian类别,它相当于一个Ñ具有足够projectives一个阿贝尔范畴的-cluster倾斜子类别。这些结果概括了Jacobsen-Jørgensen和Zhou-Zhu的工作ñ+2个角度类别。此外,当将其应用于n个精确类别时,它突出显示了新现象。

更新日期:2021-04-02
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