n-angulated quotient categories induced by mutation pairs

Lin, Zengqiang

doi:10.1007/s10587-015-0220-3

Cited by 19 publications

(14 citation statements)

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“…The notion of mutation pairs of subcategories in an (n + 2)-angulated category was defined by Lin [L,Definition 3.1]. We recall the definition here.…”

Section: Examplesmentioning

confidence: 99%

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Frobenius $n$-exangulated categories

Liu¹,

Zhou²

2019

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Herschend-Liu-Nakaoka introduced the notion of n-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of n-exangulated categories contains n-exact categories and (n+2)-angulated categories as examples. In this article, we introduce the notion of Frobenius n-exangulated categories which are a generalization of Frobenius n-exact categories. We show that the stable category of a Frobenius n-exangulated category is an (n + 2)-angulated category. As an application, this result generalizes the work by Jasso. In addition, starting from n-exangulated categories, we obatin a new n-exangulated category. This construction gives n-exangulated categories which are neither n-exact categories nor (n + 2)-angulated categories. Finally, we discuss an application of main results and give some examples illustrating our main results.

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“…The notion of mutation pairs of subcategories in an (n + 2)-angulated category was defined by Lin [L,Definition 3.1]. We recall the definition here.…”

Section: Examplesmentioning

confidence: 99%

“…Corollary 5.5. [L,Theorem 3.7] Let C be an (n + 2)-angulated category and X ⊆ A be two subcategories of C . If (A, A) is an X -mutation pair and A is extension closed, then the quotient category A/X is an (n + 2)-angulated category.…”

Section: Consider the Following Diagrammentioning

confidence: 99%

Frobenius $n$-exangulated categories

Liu¹,

Zhou²

2019

Preprint

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“…Besides, Jacobsen and Jørgensen [15], and Zhou and Zhu [22] investigated the quotient categories of n-angulated categories. For more references, see [2,4,5,9,10,16,17,19,21].…”

Section: Introductionmentioning

confidence: 99%

Ideal approximation in $n$-angulated categories

Tan¹,

Wang²,

Zhao³

2020

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We study ideal approximation theory associated to almost n-exact structures in extension closed subcategories of n-angulated categories. For n = 3, an n-angulated category is nothing but a classical triangulated category. Moreover, since every exact category can be embedded as an extension closed subcategory of a triangulated category, therefore, our approach extends the recent ideal approximations theories developed by Fu, Herzog et al. for exact categories and by Breaz and Modoi for triangulated categories.

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“…Let R be a commutative local ring with maximal principal ideal m = (p) satisfying m 2 = 0. Then the category of finitely generated free R-modules has a structure of n-angulation whenever n is even, or when n is odd and 2p = 0 in R. The theory of n-angulated categories has been developed further, we can see [3,5,12,13,14,15] for reference. In this note, we devote to provide new class of examples of n-angulated categories.…”

Section: Introductionmentioning

confidence: 99%

$n$-angulated categories from self-injective algebras

Lin

2015

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n-angulated quotient categories induced by mutation pairs

Cited by 19 publications

References 10 publications

Frobenius $n$-exangulated categories

Frobenius $n$-exangulated categories

Ideal approximation in $n$-angulated categories

$n$-angulated categories from self-injective algebras

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