Extriangulated category

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August undefined, 2024

WebClassified a possible extriangulated substructures on a given extriangulated category using functor category Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras Published in Comm. Algebra, January 2024. Links: journal, arXiv:2002.09205 WebNov 29, 2024 · Abelian categories and triangulated categories are two fundamental structures in algebra and geometry. Nakaoka and Palu [ 25] introduced the notion of extriangulated categories which is extracting properties on triangulated categories and exact categories (in particular, abelian categories).

Classifying Substructures of Extriangulated Categories via Serre ...

WebNov 1, 2024 · Extriangulated categories were introduced by Nakaoka and Palu, which unify exact categories and extension-closed subcategories of triangulated categories. In this paper, we develop the... WebMar 28, 2024 · Then we develop a general framework for c -vectors of 2-Calabi-Yau extriangulated categories with respect to arbitrary 2-cluster tilting subcategories. We … section design software

Hall algebras of extriangulated categories - ScienceDirect

Subjects: Category Theory (math.CT); Algebraic Geometry (math.AG) … WebJan 1, 2005 · Abstract. A full, extension-closed additive subcategory D of a triangulated category C in which Hom 1 C (M,N) = 0 for all M, N in D has a natural structure of exact … WebHEREDITARY EXTRIANGULATED CATEGORIES 3 (a) Ris maximal rigid: If R⊕Xis rigid, then X∈addR; (b) Ris silting: The smallest thick (that is, strictly full, closed under direct summands, and satisfying the 2-out-of-3 property for s-triangles) subcategory of C containing Ris C itself. (c) Ris tilting: There is an s-triangle P֌ R0 ։ R1 99K with R0,R1 … purina pro plan veterinary diets cc

Tilting subcategories in extriangulated categories SpringerLink

Resolving subcategories and dimensions in recollements of

WebExtriangulated categories give a simultaneous generalization of triangulated cate- gories and exact categories. In this paper, we study silting subcategories of an extriangulated … WebJan 11, 2024 · Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) subcategories in an extriangulated category is defined in this paper. purina proplan veterinary diets ha chienWebMar 14, 2024 · Extriangulated categories give a simultaneous generalization of triangulated categories and exact categories. In this paper, we study silting subcategories of an extriangulated category. First, we show that a silting subcategory induces a basis of the Grothendieck group of an extriangulated category. Secondly, we introduce the … purina pro plan under one year puppy food

"WebExtriangulated categories give a simultaneous generalization of triangulated cate- gories and exact categories. In this paper, we study silting subcategories of an extriangulated category. First, we show that a silting subcategory induces a basis of the Grothendieck group of an extriangulated category. " - Extriangulated category

Extriangulated category

Relative Auslander bijection in extriangulated categories

WebJan 11, 2024 · Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of properties in exact categories and triangulated categories. A notion … WebAug 17, 2024 · Silting reduction in extriangulated categories Authors: Yu Liu Southwest Jiaotong University Panyue Zhou Yu Zhou Tsinghua University Bin Zhu Abstract We introduce pre-silting and silting...

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WebDec 1, 2024 · A recollement of extriangulated categories is defined in [18] as a diagram of functors between extriangulated categories of the following shape satisfying some … WebMay 18, 2016 · Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories Hiroyuki Nakaoka, Yann Palu We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories.

WebExtriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we show … WebFeb 1, 2024 · In [27], Nakaoka and Palu introduced the notion of externally triangulated categories (extriangulated categories for short) as a simultaneous generalization of exact categories and...

WebFeb 18, 2024 · Stable tubes in extriangulated categories Li Wang, Jiaqun Wei, Haicheng Zhang Received April 17, 2024. Published online February 18, 2024. Abstract: Let $\mathcal{X}$ be a semibrick in an extriangulated category. If $\mathcal{X}$ is a $\tau$-semibrick, then the Auslander-Reiten quiver $\Gamma(\mathcal{F}(\mathcal{X}))$ of the … WebFeb 1, 2024 · Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we introduce and develop an analogous… 3 PDF View 2 excerpts, cites background Auslander--Reiten theory in extriangulated categories O. Iyama, H. Nakaoka, Yann …

WebJun 27, 2024 · Of course, there are extriangulated categories which are neither exact categories nor triangulated categories, see [ 12, 13 ]. Since extriangulated categories generalize both triangulated and exact categories, so one may ask if we can do a similar job on extriangulated categories.

WebMay 15, 2024 · Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact categories and triangulated categories. We consider in … section d housing loan purina pro plan veterinary diets fortifloraWebWe initiate the study of derived functors in the setting of extriangulated categories. By using coends, we adapt Yoneda's theory of higher extensions to this framework. We … purina pro plan veterinary diets for cats omWebJan 7, 2024 · The index in 2-Calabi-Yau categories was recently interpreted by Padrol, Palu, Pilaud, and Plamondon in terms of extriangulated categories. In joint work with Amit Shah, we generalise the extriangulated viewpoint and define the index of an object of a triangulated category with respect to a rigid subcategory. purina pro plan veterinary diets probioticsWebJun 23, 2024 · Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting)… Expand 25 PDF External triangulation of the homotopy category of exact quasi-category H. Nakaoka, Yann Palu Mathematics 2024 purina proplan veterinary diets om chienWebDec 1, 2024 · An extriangulated category consists of a triple (C,E,s),whereCis an additive category, Eis an additive bifunctor Communicated by Henning Krause. BHaruhisa Enomoto [email protected]... purina pro plan veterinary diets obesityWebMar 15, 2024 · Then each coheart can be naturally regarded as an extriangulated category. In this setting, if x 1 and x 2 are s-cotorsion pairs (see Definition 3.1(2)), then we have the first main theorem of this paper. Theorem 1.1 Theorem 3.6. Let C be an extriangulated category and x 1, x 2 s-cotorsion pairs. purina pro plan veterinary supplements sa