Contravariantly finite
WebMar 7, 2024 · In this paper, by using functor rings and functor categories, we study finiteness and purity of subcategories of the module categories. We give a characterisation of contravariantly finite resolving subcategories of the module category of finite representation type in terms of their functor rings. WebJan 26, 2024 · The homological theory of contravariantly finite subcategories: Auslander-Buchweitz contexts, Gorenstein categories and (co)stabilization. Comm. Algebra 28 ( 2000 ), 4547 – 4596. CrossRef Google Scholar 6 Bergh, P. A., Jørgensen, D. A. and Oppermann, S.. The Gorenstein defect category. Q. J. Math. 66 ( 2015 ), 459 – 471. CrossRef Google …
Contravariantly finite
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WebThe notion of a contravariantly finite subcategory (of the category of finitely generated modules), which is also called a (pre)covering class, was first introduced over artin algebras by Auslander and Smalø [] in connection with studying the problem of which subcategories admit almost split sequences. The notion of a resolving subcategory was introduced by … WebABSTRACT We define right n-angulated categories, which are analogous to right triangulated categories. Let 𝒞 be an additive category and 𝒳 a covariantly finite …
WebMar 1, 1991 · If A is of finite representation type, then 9°° (A) is contravariantly finite since every subcategory of mod A is contravariantly finite. In fact, A is of finite … WebJan 1, 2001 · Abstract. Let (F, G) be an adjoint pair from a category A to a category B. The contravariantly finiteness of subcategories is proved to be preserved by F, and the …
WebOct 6, 2024 · The objective of this paper is to study the relative homological properties of contravariantly and covariantly finite subcategories. Some sufficient conditions for E x t ¯ Y n A , B ≃ E x t ¯ X... WebDec 1, 2024 · It follows that T ⊥ > 0 is specially contravariantly finite in D +. Proposition 2.16. Assume that T ⊆ D ⩾ 0 is specially contravariantly finite in D + and is cosuspended such that T ˆ = D +. If T ⋂ T ⊥ > 0 is closed under products, then there is a cosilting complex T such that T = T ⊥ > 0. Proof. It is not difficult to verify that ...
Webpdn mod A is contravariantly finite in mod A. More precisely, we first prove that if the projective dimension of the injective envelope of A as a left A-module is less than or …
WebJan 27, 2024 · For a simple counterexample A consider the path algebra (over an infinite field) of the quiver. 1 ⇒ a, b 2 → c 3. modulo the relation c a = 0. This algebra has global dimension 2, so in particular the subcategory of modules of finite projective dimension is all of A -mod, which is contravariantly finite. However, the simple module S 1 has ... load bearing images of containersWebAug 23, 2024 · Every finite abelian group A is isomorphic to its dual group A ∗ := Hom ( A, C ×). The isomorphism of A with A ∗ is non-canonical, and one way to make this precise is … load bearing glueWebJun 27, 2007 · Let P (F) denote the full sucategory of A with objects the F -projective modules. If the functor F has enough F - projectives, then we show that the stable … indiana academy of ophthalmology websiteWebIn this paper, we construct a recollement of abelian categories (mod0-X,mod-X,mod-A) ( m o d 0 - X, m o d - X, m o d - A), where mod0-X m o d 0 - X is a full subcategory of mod-X m o d - X consisting of all functors vanishing on projective modules. indiana academy for science mathematicsWebIt is well-known that contravariantly finite subcategories enjoy various basic properties of the classical one (i.e. Proj R) and the subcategory GPR. Based on these results, two … indiana academy of dermatologyWebMay 1, 2014 · Let Cbe a contravariantly finite subcategory of an abelian category A. One can define the C-relative derived category of A, denoted by DC⁎(A), similarly. Rickard provided a Morita theory for derived categories. We introduce and study relative Morita theory for Gorenstein derived categories. indiana academy for sci math hmnWebApr 1, 1990 · Let A be the algebra given by the quiver 1 It is shown in [9] that these maps do not factor through an A-module of finite projective dimension, proving that P <∞ is not contravariantly finite ... load bearing internal walls