From right (n+2)-angulated categories to n-exangulated categories

The notion of right semi-equivalence in a right (n+ 2)-angulated category is defined in this article. Let C be an n-exangulated category and X is a strongly covariantly finite subcategory of C . We prove that the standard right (n + 2)-angulated category C /X is right semi-equivalence under a natural assumption. As an application, we show that a right (n + 2)-angulated category has an n-exangulated structure if and only if the suspension functor is right semi-equivalence. Besides, we also prove that an n-exangulated category C has the structure of a right (n + 2)-angulated category with right semi-equivalence if and only if for any object X ∈ C , the morphism X → 0 is a trivial inflation.

[1]  Yann Palu,et al.  External triangulation of the homotopy category of exact quasi-category , 2020, 2004.02479.

[2]  Aran Tattar,et al.  Right triangulated categories: As extriangulated categories, aisles and co-aisles , 2021, 2106.09107.

[3]  Yann Palu,et al.  Extriangulated categories, Hovey twin cotorsion pairs and model structures , 2019 .

[4]  Panyue Zhou.  A right triangulated version of Gentle-Todorov’s theorem , 2018 .

[5]  P. A. Bergh,et al.  The axioms for n–angulated categories , 2011, 1112.2533.

[6]  Jiangsheng Hu,et al.  Proper classes and Gorensteinness in extriangulated categories , 2019, Journal of Algebra.

[7]  H. Nakaoka,et al.  n-exangulated categories (I): Definitions and fundamental properties , 2020 .

[8]  Jiaqun Wei,et al.  (n + 2)-Angulated Quotient Categories , 2019 .

[9]  Steffen Oppermann,et al.  n-angulated categories , 2010, 1006.4592.

[10]  Apostolos Beligiannis,et al.  Left triangulated categories arising from contravariantly finite subcategories , 1994 .

[11]  Yu Liu,et al.  From n-exangulated categories to n-abelian categories , 2020, 2006.02223.

[12]  Panyue Zhou,et al.  Triangulated quotient categories revisited , 2016, 1608.00297.

[13]  G. Jasso,et al.  n-Abelian and n-exact categories , 2014, 1405.7805.

[14]  Panyue Zhou,et al.  Two new classes of n-exangulated categories , 2021, Journal of Algebra.

[15]  Zengqiang Lin.  Right n-angulated categories arising from covariantly finite subcategories , 2014, 1409.2948.