Gorenstein objects in triangulated categories
WebJan 26, 2024 · We apply the Auslander–Buchweitz approximation theory to show that the Iyama and Yoshino's subfactor triangulated category can be realized as a triangulated … WebNov 30, 2024 · This thesis mainly studies the relative Gorenstein objects in the extriangulated category $\mathcal {C}$ with a proper class $\xi$ and the related properties of these objects. In the first part ...
Gorenstein objects in triangulated categories
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Webunbounded derived category D(A), where A is a ring. Given a non-empty set Sof objects in D(A), the localizing (resp. colocalizing)subcategorygeneratedbyS, denotedbyLoc(S) (resp. Coloc(S)), is bythedefinitionthe smallest full triangulated subcategory of D(A) which contains Sand is closed under infinite coproducts (resp. products). We 1 WebIn this paper, we introduce the notion of $\mathcal{W}$-Gorenstein objects and $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object in $\mathcal{C}$ and study the properties of $\mathcal{W}$-Gorenstein objects and characterize the finite $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object. Some applications …
WebMar 19, 2016 · The fully exact subcategory F of fibrant objects is a Frobenius category with its projective-injective objects being precisely the injective objects of A. (3) The … WebGorenstein projective modules and Gorenstein injective modules in triangulated categories. We prove that the stable category Gω, where Gω is the subcategory of all ω-Gorenstein objects, is a triangulated category and it is, under some conditions, triangle equivalent to the relative singularity category of T with respect to ω.
WebMar 14, 2024 · Positive Fuss–Catalan Numbers and Simple-Minded Systems in Negative Calabi–Yau Categories Web北京师范大学数学科学学院教育部数学与复杂系统重点实验室代数年活动之二:表示论研讨会,2014年11月12日.Miniworkshop on Representation Theory Nov. 12, 2014ProgramNovember
WebKeywords: triangulated categories, a proper class of triangles, resolving resolution dimensions, resolving subcategories, Auslander-Buchweitz approximations MSC 2024: 18G20, 18G25, 18G10 ... Asadollahi and Salarian [13] introduced the notion of ξ-Gorenstein projective objects.
WebDec 15, 2015 · Download PDF Abstract: We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection with t-structures generated by their co-heart whose heart has a generator, and … new years eve party flyer templateWebJan 6, 2024 · The notion of extriangulated categories was introduced by Nakaoka and Palu in [] as a simultaneous generalization of exact categories and triangulated categories.Exact categories and extension closed subcategories of an extriangulated category are extriangulated categories, while there exist some other examples of … new years eve party fredericksburg txWebAug 1, 2024 · There is a cofibrantly generated abelian model structure on R-Mod in which every object is cofibrant and the fibrant objects are the Gorenstein (L, A)-injective modules. The trivially fibrant objects are the categorically injective modules. ... We point out that the homotopy categories of these model structures are well generated triangulated ... new years eve party games freeWebJan 9, 2024 · Sather-Wagstaff S, Sharif T, White D. Stability of Gorenstein categories. J Lond Math Soc, 2008, 77: 481–502. Article MathSciNet Google Scholar Wang Z P, Guo S T, Liang C L. Stability of Gorenstein objects in triangulated categories. Sci Sin Math (Chin Ser), 2024, 47: 349–356 (in Chinese) mildest shampoo for color treated hairWeb-Gorenstein objects In this paper, we x a proper class of triangles ˘ in a triangulated category. C. Recall that for any object of. C. in. C. and any integer. n 0, the ˘-extension … mildest weather in united statesWebApr 25, 2015 · Download PDF Abstract: We study singularity categories through Gorenstein objects in triangulated categories and silting theory. Let ${\omega}$ be a semi-selforthogonal (or presilting) subcategory of a triangulated category $\mathcal{T}$. We introduce the notion of $\omega$-Gorenstein objects, which is far extended version … new years eve party hornsWebC(R), is a Frobenius category with projective-injective objects all R-modules in F C(R) ∩ C C(R). Therefore, the stable category G CF(R)∩ B C(R)∩ C C(R) is a triangulated category. From the point of view of homotopy theory, it is natural to ask whether there is a hereditary abelian model structure that models this stable category. new years eve party gift basket