Cluster tilting subcategories

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August undefined, 2024

WebJan 15, 2011 · Abstract. The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n -Auslander–Reiten translation functor τ n plays an important role in the study of n -cluster tilting subcategories. We study the category M n of preinjective-like … WebAug 10, 2024 · Abstract. We investigate abelian quotients arising from extriangulated categories via morphism categories, which is a unified treatment for both exact categories and triangulated categories. Let (\mathcal {C},\mathbb {E},\mathfrak {s}) be an extriangulated category with enough projectives \mathcal {P} and {\mathscr {M}} be a full …

Cluster tilting subcategories and torsion pairs in …

WebTRIANGULATED CATEGORIES WITH CLUSTER TILTING SUBCATEGORIES 705 then weak add.TT1U/-cluster tilting subcategories coincide with add.TT1U/-cluster tilting subcategories, and are also the same as TT1U-cluster tilting objects introduced in[Yang and Zhu 2024]. The ﬁrst part of our work is to develop a basic theory of ghost cluster … WebMay 12, 2024 · Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. 100% of your contribution will fund improvements and new initiatives to benefit arXiv's global scientific community. 99味常用中药入门

[2010.13203] Higher Ideal Approximation Theory - arXiv.org

WebJul 2, 2024 · We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra contains a -cluster tilting subcategory for some , then is a radical square zero Nakayama algebra. This gives a complete classification of weakly -representation finite gentle algebras ... WebAug 2, 2012 · Suppose that X is a cluster tilting subcategory of C and A is the abelian quotient category C /X . Then: (1) The category A has enough projective objects and enough injective objects. (2) Let ΣX ... 99和98

Cluster tilting subcategories and torsion pairs in …

Abelian Categories Arising from Cluster Tilting Subcategories

WebNov 20, 2024 · In particular, it has cluster tilting subcategories, classified by Gratz, Holm and Jørgensen in [GHJ19], given by suitable triangulations of the closed disc with marked points Z. While providing ... WebApr 1, 2024 · Since for any d ≥ 1 there exist examples of d-cluster tilting subcategories without any non-zero projective or injective objects, see [22], the result is necessary to complete the axiomatization of d-cluster tilting subcategories in terms of d-abelian categories. Corollary 1.3. Let X be an additive category. The following hold: (i) 99味精WebJul 30, 2024 · In this article, we find a one-to-one correspondence between support τ -tilting (resp. τ -rigid) subcategories of / and maximal relative rigid (resp. relative rigid) subcategories of , and show that support tilting subcategories in / is a special kind of support τ -tilting subcategories. We also study the relation between tilting ... 99咳咳

"WebJun 13, 2024 · In this paper we introduce nZ-abelian and nZ-exact categories by axiomatising properties of nZ-cluster tilting subcategories. We study this categories and show that every nZ-cluster tilting … Expand. PDF. View 3 excerpts, cites background; Save. Alert. The role of gentle algebras in higher homological algebra. " - Cluster tilting subcategories

Cluster tilting subcategories

Abelian categories arising from cluster tilting …

WebMay 2, 2024 · We also introduce mixed (pre)cluster tilting modules as a generalisation of (pre)cluster tilting modules, and establish an Auslander type correspondence by showing that dominant Auslander ... http://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf

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WebIn particular, we shall show that the cluster-tilting subcategories are precisely given by compact tri- angulations. We first study the (canonical) orbit category of the bounded de- rived category of finite dimensional representations of a quiver with no infinite path, and we pay more attention on the case where the quiver is of infinite Dynkin ... Webthis we introduce cluster tilting subcategories of left triangulated categories, and we show that there is a correspondence between cluster tilting subcategories of Eand .Wealso …

WebJun 8, 2024 · In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type A ∞ as introduced by Holm-Jørgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim. WebNov 12, 2024 · Wuzhong Yang, Panyue Zhou, Bin Zhu. Let $\C$ be a triangulated category with a cluster tilting subcategory $\T$ . We introduce the notion of $\T [1]$ -cluster …

WebOct 25, 2024 · On the other hand, ideal approximation theory, that is a gentle generalization of the classical approximation theory and deals with morphisms and ideals instead of objects and subcategories, is an active area that has been the subject of several researches. Our aim in this paper is to introduce the so-called `ideal approximation theory' into ... Webimal rigid subcategories, we prove that the converse is true if the 2-Calabi-Yau extri-angulated categories admit a cluster tilting subcategories, which generalizes a result …

WebMar 13, 2024 · • Cluster categories endowed with a ﬁxed cluster tilting object, and the maximal r ela- tive extriangulated structure making it pr ojective. In this case, the silting ob jects are

WebMoreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that … 99和99a区别WebMay 2, 2024 · Laertis Vaso. We give a characterization of -cluster tilting subcategories of representation-directed algebras based on the -Auslander-Reiten translations. As an application we classify acyclic Nakayama algebras with homogeneous relations which admit an -cluster tilting subcategory. Finally, we classify Nakayama algebras of global … 99和96坦克WebMay 2, 2024 · Laertis Vaso. We give a characterization of -cluster tilting subcategories of representation-directed algebras based on the -Auslander-Reiten translations. As an … 99哩漫WebCluster tilting subcategories are obviously strongly functorially finite maximal rigid subcategories, we prove that the converse is true if the 2-Calabi-Yau extriangulated categories admit a cluster tilting subcategories, which generalizes a result of Buan-Iyama-Reiten-Scott [BIRS] and Zhou-Zhu [ZZ]. ... 99啦啦WebAug 1, 2024 · Moreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2 ... 99回薬剤師国家試験 113WebMoreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2-Calabi-Yau triangulated category ℬ , a functorially finite, extension closed subcategory 𝒯 of ℬ is cluster tilting if and only if ℬ /𝒯 is an ... 99品牌WebSep 1, 2024 · Let $ \mathscr{B} $ be an extriangulated category which admits a cluster tilting subcategory $ \mathcal{T} $. We firstly introduce notions of $ \mathcal{T} $-cluster tilting subcategories and ... 99回箱根駅伝復路優勝