Corpus ID: 235458352

Right triangulated categories: As extriangulated categories, aisles and co-aisles

@inproceedings{Tattar2021RightTC,
  title={Right triangulated categories: As extriangulated categories, aisles and co-aisles},
  author={A. Tattar},
  year={2021}
}
Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories have a natural extriangulated structure and are appearing as the (co-)aisle of a (co-)t-structure in an associated triangulated category. 
From right (n+2)-angulated categories to n-exangulated categories
  • Jian He, Panyue Zhou
  • Mathematics
  • 2021
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 . WeExpand

References

SHOWING 1-10 OF 56 REFERENCES
Extriangulated categories, Hovey twin cotorsion pairs and model structures
We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories.Expand
Definability and approximations in triangulated categories
We give criteria for subcategories of a compactly generated algebraic triangulated category to be precovering or preenveloping. These criteria are formulated in terms of closure conditions involvingExpand
Torsion pairs in silting theory
In the setting of compactly generated triangulated categories, we show that the heart of a (co)silting t-structure is a Grothendieck category if and only if the (co)silting object satisfies a purityExpand
Mutation in triangulated categories and rigid Cohen–Macaulay modules
We introduce the notion of mutation of n-cluster tilting subcategories in a triangulated category with Auslander–Reiten–Serre duality. Using this idea, we are able to obtain the completeExpand
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-projectiveExpand
The triangulation of the subfactor categories of additive categories with suspensions
We provide a framework to triangulate subfactor categories of additive categories with additive endofunctors. It is proved that such a framework is sufficiently flexible to cover many instances inExpand
Hearts of twin Cotorsion pairs on extriangulated categories
In this article, we study the heart of a cotorsion pairs on an exact category and a triangulated category in a unified meathod, by means of the notion of an extriangulated category. We prove that theExpand
On exact categories and applications to triangulated adjoints and model structures
Abstract We show that Quillenʼs small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence ofExpand
General Heart Construction on a Triangulated Category (I): Unifying t-Structures and Cluster Tilting Subcategories
  • H. Nakaoka
  • Mathematics, Computer Science
  • Appl. Categorical Struct.
  • 2011
TLDR
Koenig and Zhu showed in detail, how the abelian structure is given on this quotient category, in a more abstract setting, using the notion of a cotorsion pair. Expand
Classifying Substructures of Extriangulated Categories via Serre Subcategories
We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar way to the author'sExpand
...
1
2
3
4
5
...