Triangulated quotient categories revisited

@article{Zhou2016TriangulatedQC,
  title={Triangulated quotient categories revisited},
  author={Panyue Zhou and Bin Zhu},
  journal={arXiv: Representation Theory},
  year={2016}
}

Abelian Quotients Arising from Extriangulated Categories via Morphism Categories

We investigate abelian quotients arising from extriangulated categories via morphism categories, which is a unified treatment for both exact categories and triangulated categories. Let

QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES

Abstract The notion of mutation pairs of subcategories in an n-abelian category is defined in this paper. Let ${\cal D} \subseteq {\cal Z}$ be subcategories of an n-abelian category ${\cal A}$. Then

Gorenstein Homological Dimensions for Extriangulated Categories

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. The authors introduced and studied $\xi$-$\mathcal{G}$projective and

Proper resolutions and Gorensteinness in extriangulated categories

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles, and $\mathcal{W}$ an additive full subcategory of $\mathcal C$. We

Relative rigid subcategories and $\tau$-tilting theory

Let $\mathcal B$ be an extriangulated category with enough projectives $\mathcal P$ and enough injectives $\mathcal I$, and let $\mathcal R$ be a contravariantly finite rigid subcategory of $\mathcal

Gorenstein Objects in extriangulated Categories

This paper mainly studies the relative Gorenstein objects in the extriangulated category $\mathcal{C}=(\mathcal{C},\mathbb{E},\mathfrak{s})$ with a proper class $\xi$ and the related properties of

Abelian quotients of extriangulated categories

AbstractWe prove that certain subquotient categories of extriangulated categories are abelian. As a particular case, if an extriangulated category $$\mathscr {C}$$C has a cluster-tilting subcategory

Auslander's defects over extriangulated categories: An application for the general heart construction

  • Yasuaki Ogawa
  • Mathematics
    Journal of the Mathematical Society of Japan
  • 2021
The notion of extriangulated category was introduced by Nakaoka and Palu giving a simultaneous generalization of exact categories and triangulated categories. Our first aim is to provide an extension
...

References

SHOWING 1-10 OF 27 REFERENCES

Rigid objects, triangulated subfactors and abelian localizations

We show that the abelian category $$\mathsf{mod}\text{-}\mathcal{X }$$ of coherent functors over a contravariantly finite rigid subcategory $$\mathcal{X }$$ in a triangulated category $$\mathcal{T

The model structure of Iyama-Yoshino's subfactor triangulated categories

Let $\X$ be a homological finite subcategory of an additive category $\C$. Under suitable conditions, we prove that the stable category $\C/\X$ as the homotopy category of a closed model structure on

Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories

We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories.

Triangulated quotient categories

A notion of mutation of subcategories in a right triangulated category is defined in this paper. When (Z,Z) is a D−mutation pair in a right triangulated category C, the quotient category Z/D carries

Left triangulated categories arising from contravariantly finite subcategories

Let modA be the category of finitely generated right A-modules over an artin algebra ⋀, and F be an additive subfunctor of . Let P(F) denote the full sucategory of A with objects the F-projective

Derived Categories and Their Uses

Exact Categories

Mutation Pairs in Abelian Categories

A notion of mutation pairs of subcategories in an abelian category is defined in this article. For an extension closed subcategory 𝒵 and a rigid subcategory 𝒟 ⊂ 𝒵, the subfactor category 𝒵/[𝒟]

Three results on Frobenius categories

This paper consists of three results on Frobenius categories: (1) we give sufficient conditions on when a factor category of a Frobenius category is still a Frobenius category; (2) we show that any