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1.
对给定的两个伴随对,本文利用Godement积给出其上函子范畴的伴随对.进一步地,本文证明:如果一个预加范畴的recollement满足加法函数j~*是满的,则该recollement可以自然诱导其上模范畴的一个阿贝尔范畴的recollement.该结果从范畴的角度给出了三角矩阵环可自然具有recollement的一个新解释.  相似文献   

2.
郑敏  陈清华 《数学进展》2014,(2):243-254
讨论在一定条件下Abel范畴的recollement经过范畴的平凡扩张可诱导出一个新recollement的问题.将结果应用到环上的模范畴,得到平凡(单点)扩张环具有Morita等价不变性;结合加法范畴的幂等完备化,构造出一个幂等完备化范畴关于范畴平凡扩张的recollement.  相似文献   

3.
证明了三角范畴的recollement可以自然诱导其商范畴的recollement.特别地,得到类似于群同态第二基本定理的结果,即若U是三角范畴D的局部化(或余局部化)子范畴,V是U的三角满子范畴,则U/V是D/V的局部化(或余局部化)子范畴,并且有三角等价(D/V)/(U/V)≌D/U.同理,对Abel范畴的recollement也有相应的结果.  相似文献   

4.
文章研究了三角范畴D及其coherent函子范畴A(D)的recollement之间的关系.利用D的recollement可以诱导A(D)的prerecollement,文章证明了该prerecollement是recollement的充分必要条件是D的recollement是可裂的;并且D的recollement可以诱导A(D)的prerecollement.  相似文献   

5.
林增强 《数学研究》2010,43(2):193-197
函子范畴是—类重要的范畴,因为许多常见的范畴都是函子范畴,并且任意给定的范畴都可以通过Yoneda引理嵌入到一个函子范畴,而函子范畴具有比原范畴更好的性质。本文证明了Abel范畴的recollement可以自然诱导两类函子范畴的recollment.应用到k-线性范畴,得到k.线性Abel范畴的recollement可以自然诱导其模范畴的recollement.  相似文献   

6.
林记 《数学杂志》2016,36(6):1201-1208
文章研究了三角范畴D及其coherent函子范畴A(D)的recollement之间的关系.利用D的recollement可以诱导A(D)的prerecollement,文章证明了该prerecollement是recollement的充分必要条件是D的recollement是可裂的;并且D的recollement可以诱导A(D)的prerecollement.  相似文献   

7.
从三角范畴的recollement到Abel范畴的recollement   总被引:1,自引:0,他引:1  
王敏雄  林亚南 《中国科学A辑》2009,39(10):1180-1186
研究了三角范畴的recollement与Abel范畴的recollement的关系.证明了:若三角范畴D允许关于三角范畴D和D的recollement,则Abel范畴D/T允许关于Abel范畴D/i^*(T)和D/j^*(T)的recollement,其中T为D的cluster-倾斜子范畴,且满足i*i^*(T)*T,j^*j^*(T)^*T.  相似文献   

8.
陈清华 《数学进展》2008,37(2):189-196
若代数A和B导出等价,则它们的Repetitive代数A和B也是导出等价,从而是稳定等价.这样利用更直接的代数方法完全回答了H.Asashiba提出的问题,并推广了Rickard,杜先能,Tachikawa-Wakamatsu等人的相应结果.进而,把以上结果推广到上有界复形的导出范畴的对称recollement的情形.  相似文献   

9.
研究有限维代数的有限生成模范畴之间的recollement. 证明了: 对于3个代数A, B, C, 若$A$的模范畴允许有关于B的模范畴和C的模范畴的recollement, 则A的单点扩张代数的模范畴允许有关于B的单点扩张代数的模范畴和C的模范畴的recollement.  相似文献   

10.
在交换环R上,引入了Clean-正合以及Clean-导出范畴的概念,分别给出了Clean-短正合列和Clean-正合复形的等价刻画,研究了Clean-导出范畴的性质.特别地,证明了有界Clean-导出范畴可以实现为特殊的同伦范畴.  相似文献   

11.
The concept of recollement is used to obtain a stratification of the derived module category of a ring which may be regarded as an analogue of a composition series for groups or modules. This analogy raises the problem whether a ‘derived’ Jordan Hölder theorem holds true; that is, are such stratifications unique up to ordering and equivalence? This is indeed the case for several classes of rings, including semi-simple rings, commutative Noetherian rings, group algebras of finite groups, and finite dimensional algebras which are piecewise hereditary.  相似文献   

12.
We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.  相似文献   

13.
We first prove that the idempotent completion of a right or left recollement of triangulated categories is still a right or left recollement, then show that the t-structure on a triangulated category is compatible with taking idempotent completion. Finally, an application of the main theorem is given, which is focused on the boundedness and nondegeneration of the t-structure induced by a recollement and its idempotent completion.  相似文献   

14.
Let A be a finite-dimensional algebra over arbitrary base field k. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite-dimensional k-algebras B and C:D- (Mod - B) D-(Mod - A) D-(Mod - C),then the unbounded derived module category D-(Mod - T(A)) admits symmetric recollement relative to the unbounded derived module categories of T(B) and T(C):D-(Mod - T(B)) D-(Mod - T(A)) D-(Mod -T(C)).  相似文献   

15.
We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [Math. Ann., 2012, 353: 765–781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.  相似文献   

16.
In this paper we reconsider a classical theorem by Bican and El Bashir, which guarantees the existence of non-trivial relatively pure submodules in a module category over a ring with unit. Our aim is to generalize the theorem to module categories over rings with several objects. As an application, we then consider the special case of α-pure objects in such module categories.  相似文献   

17.
This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category \(\mathcal {S}\) and a maximal object s of \(\mathcal {S}\) and construct a recollement of \(\text {Mod-}\mathcal {S}\) in terms of \(\text {Mod-End}_{\mathcal {S}}(s)\) and \(\text {Mod-}(\mathcal {S}\setminus \{s\})\) in four different levels. In case \(\mathcal {S}\) is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N-complexes.  相似文献   

18.
我们在本文中引入了Abel范畴的右双-Giraud粘合定义.我们证明了右双-Giraud粘合与余遗传和遗传的挠对存在着双射对应.此外,我们通过模范畴中特定的幂等理想刻画了这类挠对.  相似文献   

19.
辛林  郑琳 《数学杂志》2016,36(4):820-830
本文研究广义Comma范畴上Recollement问题.利用Abel范畴上Recollement及其伴随函子,诱导出广义Comma范畴,并利用比较函子构造出广义Comma范畴上的Recollement.这些结果推广了一般Abel范畴上的Recollement,丰富了Comma范畴研究.  相似文献   

20.
We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz–Happel’s theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen–Macaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed.  相似文献   

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