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 … WebJun 1, 2024 · In an attempt to develop the Beligiannis' theory, Asadollahi and Salarian [1] introduced and studied ξ-Gorenstein projective and injective objects in triangulated categories with a proper class ξ, which share basic properties with Gorenstein projective and injective modules. Our next aim of this paper is to contribute in developing the above ...
Gorenstein objects in triangulated categories
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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. 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 …
WebMar 14, 2024 · Positive Fuss–Catalan Numbers and Simple-Minded Systems in Negative Calabi–Yau Categories 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 …
WebMar 31, 2015 · If D is a 2-CY triangulated category, then it turns out that T [1]-tilting objects are precisely cluster-tilting objects. Thus this theorem improv es a result in [AIR]. 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 …
WebApr 25, 2015 · Let ${\omega}$ be a semi-selforthogonal (or presilting) subcategory of a triangulated category $\mathcal{T}$. We introduce the notion of $\omega$-Gorenstein …
WebC(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. is there going to be a season 4 of victoriaWebApr 28, 2024 · we give some criteria for identifying a triangulated catgory to be Gorenstein and an artin algebra to be F -Gorenstein. Keywords: complete cohomology; balance; extriangulated category; prop er class. ikea cuisine four encastrableWebRelated properties. For a Gorenstein scheme X of finite type over a field, f: X → Spec(k), the dualizing complex f! (k) on X is a line bundle (called the canonical bundle K X), … ikea cuisine meuble bas angleWebJun 1, 2024 · Then: (1) The (additive) quotient category C / X is an n-abelian category. (2) C / X is an n-cluster-tilting subcategory of mod ( Σ − n X). (3) If C is a k-linear Hom-finite with a Serre functor, then the category mod ( Σ − n X) is a Gorenstein category, that is, each injective object has projective dimension ≤ n, and each projective ... ikea cuisine meuble bas 20 cmWebthe category of Gorenstein projective E-modules [AB69,EJ00]. Here is the syzygy functor of modE. This is a Frobenius category with projEthe subcategory of projective objects. Remark 2.1. The objects of GP(E) are sometimes called Cohen{Macaulay modules, but there are reasons why we do not do this; see Remark3.3below. They are sometimes also ... ikea cuddly toysWebAug 1, 2024 · We prove that the stable category G ω _: = G ω / add ω of G ω modulo addω, where G ω is the subcategory of all ω-Gorenstein objects, is a triangulated category. Moreover, we prove that, under some conditions, the triangulated category G ω _ is triangle equivalent to the relative singularity category of T with respect to the thick ... ikea cuisine evier inoxWebApr 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 … is there going to be a season 5 of jessie