共查询到20条相似文献,搜索用时 31 毫秒
1.
Ya-nan LIN & Lin XIN Department of Mathematics Xiamen University Xiamen China Department of Mathematics Fujian Normal University Puzhou China 《中国科学A辑(英文版)》2007,50(1):13-26
Motivated by the concept of a torsion pair in a pre-triangulated category induced by Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated category is introduced and investigated. We provide new connections between different aspects of torsion pairs in one-sided triangulated categories, pre-triangulated categories, stable categories and derived categories. 相似文献
2.
Extriangulated category was introduced by H.Nakaoka and Y.Palu to give a unification of properties in exact categories anjd triangulated categories.A notion of tilting(resp.,cotilting)subcategories in an extriangulated category is defined in this paper.We give a Bazzoni characterization of tilting(resp.,cotilting)subcategories and obtain an Auslander-Reiten correspondence between tilting(resp.,cotilting)subcategories and coresolving covariantly(resp.,resolving contravariantly)finite subcatgories which are closed under direct summands and satisfy some cogenerating(resp.,generating)conditions.Applications of the results are given:we show that tilting(resp.,cotilting)subcategories defined here unify many previous works about tilting modules(subcategories)in module categories of Artin algebras and in abelian categories admitting a cotorsion triples;we also show that the results work for the triangulated categories with a proper class of triangles introduced by A.Beligiannis. 相似文献
3.
《Journal of Pure and Applied Algebra》2022,226(11):107092
We study the existence of almost split sequences in tri-exact categories, that is, extension-closed subcategories of triangulated categories. Our results unify and extend a number of existence theorems for almost split sequences in abelian categories and exact categories (that is, extension-closed subcategories of abelian categories), and those for almost split triangles in triangulated categories by numerous researchers. As applications, we obtain some new results on the existence of almost split triangles in the derived categories of all modules over an algebra with a unity or a locally finite dimensional algebra given by a quiver with relations. 相似文献
4.
A recollement is a decomposition of a given category (abelian or triangulated) into two subcategories with functorial data that enables the glueing of structural information. This paper is dedicated to investigating the behaviour under glueing of some basic properties of abelian categories (well-poweredness, Grothendieck's axioms AB3, AB4 and AB5, existence of a generator) in the presence of a recollement. In particular, we observe that in a recollement of a Grothendieck abelian category the other two categories involved are also Grothendieck abelian and, more significantly, we provide an example where the converse does not hold and explore multiple sufficient conditions for it to hold. 相似文献
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6.
For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A) are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A (×) K[X]/(XN) for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories. 相似文献
7.
Georg Biedermann 《Journal of Pure and Applied Algebra》2007,208(2):497-530
For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions, we construct a tower of interpolation categories. These are categories over which the functor factorizes and which capture more and more information according to the injective dimension of the images of the functor. The categories are obtained by using truncated versions of resolution model structures. Examples of functors fitting in our framework are given by every generalized homology theory represented by a ring spectrum satisfying the Adams-Atiyah condition. The constructions are closely related to the modified Adams spectral sequence and give a very conceptual approach to the associated moduli problem and obstruction theory. As an application, we establish an isomorphism between certain E(n)-local Picard groups and some Ext-groups. 相似文献
8.
Marco Porta 《Advances in Mathematics》2010,225(3):1669-1715
The Popescu-Gabriel theorem states that each Grothendieck abelian category is a localization of a module category. In this paper, we prove an analogue where Grothendieck abelian categories are replaced by triangulated categories which are well generated (in the sense of Neeman) and algebraic (in the sense of Keller). The role of module categories is played by derived categories of small differential graded categories. An analogous result for topological triangulated categories has recently been obtained by A. Heider. 相似文献
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10.
Hiroyuki Nakaoka 《Applied Categorical Structures》2011,19(6):879-899
In the paper of Keller and Reiten, it was shown that the quotient of a triangulated category (with some conditions) by a cluster
tilting subcategory becomes an abelian category. After that, Koenig and Zhu showed in detail, how the abelian structure is
given on this quotient category, in a more abstract setting. On the other hand, as is well known since 1980s, the heart of
any t-structure is abelian. We unify these two constructions by using the notion of a cotorsion pair. To any cotorsion pair in
a triangulated category, we can naturally associate an abelian category, which gives back each of the above two abelian categories,
when the cotorsion pair comes from a cluster tilting subcategory, or a t-structure, respectively. 相似文献
11.
Mark Hovey 《Mathematische Zeitschrift》2002,241(3):553-592
We make a general study of Quillen model structures on abelian categories. We show that they are closely related to cotorsion
pairs, which were introduced by Salce [Sal79] and have been much studied recently by Enochs and coauthors [EJ00]. This gives
a method of constructing model structures on abelian categories, which we illustrate by building two model structures on the
category of modules over a (possibly noncommutative) Gorenstein ring. The homotopy category of these model structures is a
generalization of the stable module category much used in modular representation theory. This stable module category has also
been studied by Benson [Ben97].
Received: 14 December 2000; in final form: 17 December 2001 / Published online: 5 September 2002 相似文献
12.
A notion of mutation of subcategories in a right triangulated category is defined in this article. When (𝒵, 𝒵) is a 𝒟-mutation pair in a right triangulated category 𝒞, the quotient category 𝒵/𝒟 carries naturally a right triangulated structure. Moreover, if the right triangulated category satisfies some reasonable conditions, then the right triangulated quotient category 𝒵/𝒟 becomes a triangulated category. When 𝒞 is triangulated, our result unifies the constructions of the quotient triangulated categories by Iyama-Yoshino and by Jørgensen, respectively. 相似文献
13.
Mustafa Kemal Berktaş Septimiu Crivei Fatma Kaynarca Derya Keskin Tütüncü 《Journal of Pure and Applied Algebra》2021,225(6):106621
Two uniqueness theorems on uniform decompositions due to Krause, Diracca and Facchini are extended from abelian categories to weakly idempotent complete exact categories. We give applications to (quasi-)abelian categories, finitely accessible additive categories and exactly definable additive categories. 相似文献
14.
XiaoJuan Zhao 《中国科学 数学(英文版)》2014,57(11):2329-2334
Let A and B be finite-dimensional algebras over a field k of finite global dimension. Using some results of Gorsky in “Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras”, we prove that if A and B are derived equivalent, then the corresponding m-periodic derived categories are triangulated equivalent. 相似文献
15.
Hans-Joachim Baues 《Journal of Pure and Applied Algebra》2007,211(3):821-850
We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues-Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category. 相似文献
16.
We introduce a notion of an extended operation which should serve as a new tool for the study of categories like Mal’tsev, unital, strongly unital and subtractive categories.
However, in the present paper we are only concerned with subtractive categories, and accordingly, most of the time we will
deal with extended subtractions, which are particular instances of extended operations. We show that these extended subtractions provide new conceptual characterizations
of subtractive categories and moreover, they give an enlarged “algebraic tool” for working in a subtractive category—we demonstrate
this by using them to describe the construction of associated abelian objects in regular subtractive categories with finite colimits. Also, the definition and some basic properties of abelian objects
in a general subtractive category is given for the first time in the present paper.
The second author acknowledges the support of Claude Leon Foundation, INTAS (06-1000017-8609) and Georgian National Science
Foundation (GNSF/ST06/3-004). 相似文献
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Simion Breaz 《Czechoslovak Mathematical Journal》2005,55(1):133-144
We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories. 相似文献
19.
《Mathematische Nachrichten》2017,290(10):1512-1530
From certain triangle functors, called nonnegative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the stable categories of the abelian categories. The construction generalizes a previous work by Hu and Xi. We show that the stable functors of nonnegative functors have nice exactness property and are compatible with composition of functors. This allows us to compare conveniently the homological properties of objects linked by the stable functors. In particular, we prove that the stable functor of a derived equivalence between two arbitrary rings provides an explicit triangle equivalence between the stable categories of Gorenstein projective modules. This generalizes a result of Y. Kato. Our results can also be applied to provide shorter proofs of some known results on homological conjectures. 相似文献
20.
《Journal of Pure and Applied Algebra》2022,226(4):106862
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated. 相似文献