Gorenstein objects in triangulated categories
Websummands. We investigate when the triangulated homotopy cate-gory K(X) is compactly generated, and give a number of examples. Introduction Let X be a class of left R–modules which is closed under set-indexed coproducts and direct summands. When the (triangulated) homotopy category K(X) associated to X is compactly generated, it can … 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 …
Gorenstein objects in triangulated categories
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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 ... WebSep 25, 2014 · Let $\\mathcal{C}$ be a triangulated category with a proper class $ξ$ of triangles. Asadollahi and Salarian introduced and studied $ξ$-Gorenstein projective and …
Webmological properties for a triangulated category. First, we discuss the stability of ξ-Gorenstein projective objects, and show that the subcategory GP(ξ) of all ξ-Gorenstein projective objects has a strong stability. That is, an iteration of the procedure used to define the ξ-Gorenstein projec-tive objects yields exactly the ξ-Gorenstein ... WebJan 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)
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 … WebMay 1, 2024 · Introduction. In [1], Adachi, Iyama and Reiten introduced a generalization of classical tilting theory, which is called τ-tilting theory.They proved that for a 2-Calabi-Yau triangulated category C with a cluster tilting object T, there exists a bijection between the basic cluster tilting objects in C and the basic support τ-tilting modules in mod End C (T) …
WebJan 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 …
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 … rowington mens clubWebAug 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 ... stream twitch on tiktokWebWe study criteria for a ring – or more generally, for a small category – to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the … stream twitter feedWebIn this paper, we introduce the notion of $\mathcal{W}$-Gorenstein objects and $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object in $\mathcal{C}$ … rowing toolWebJun 26, 2024 · Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. A notion of proper class in an extriangulated category is defined in this paper. Let $\\mathcal{C}$ be an extriangulated category and $ξ$ a proper class in $\\mathcal{C}$. We prove that … rowington play cricketstream twitch sur ipadWebJul 15, 2014 · 4. Gorenstein derived functors and global Gorenstein dimension for triangulated categories. In this section, we first define E -Gorenstein derived functors … stream two of us