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

2021/08/18 by He, Jian, Zhou, Panyue
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2108.07985

Abstract

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

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