首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
The notion of the root of the category, which is a minimal (in a precise sense) weakly coreflective subcategory, is introduced in view of defining local solutions of universal problems: If U is a functor from C to C and c an object of C, the root of the comma-category c|U is called a U-universal root generated by c; when it exists, it is unique (up to isomorphism) and determines a particular form of the locally free diagrams defined by Guitart and Lair. In this case, the analogue of an adjoint functor is an adjoint-root functor of U, taking its values in the category of pro-objects of C. Local colimits are obtained if U is the insertion from a category into its category of ind-objects; they generalize Diers' multicolimits. Applications to posets and Galois theory are given.  相似文献   

2.
3.
黎奇升  佟文廷 《数学进展》2004,33(2):236-242
本文证明了:(1)Exchange环R的K0群的正向凸子群格同构于R的稳定余有限半本原理想格;(2)稳定有限、半本原的exchange环R是单的当且仅当它是K0-单的并且满足逼近弱s^*—可比性,推广了Goodearl,Ara等人的结果。  相似文献   

4.
We present two related categorical constructions. Given a category C, we construct a category C[d], the category of directed systems in C. C embeds into C[d], and if C has enough colimits, then C is monadic over C[d]. Also, if E,M is a factorization structure for C, then C[d] has a related factorization structure Ed Md such that if E consists entirely of monic arrows, then so does Ed and the Ed-quotient poset of an object A is naturally the poset of directed downsets of the E-quotient poset of A. Similarly, if M consists entirely of monicarrows, then so does Md and the Md-subobject poset of an object A is naturally the poset of directed downsets of the M-subobject poset. C[d] has completeness and cocompleteness properties at least as good as those of C, and it is abelian if C is. Dualization gives the other construction: a category C[i], the category of inverse systems in C, into which C also embeds and which satisfies similar properties, except that directed downsets in the E-quotient and M-subobject posets are replaced by directed upsets.  相似文献   

5.
We provide a counterexample to a theorem of Ford, namely a pushout square of categories with all involved functors injective, such that there is no associated exact “Mayer–Vietoris” sequence of derived limits. Further, we construct a Mayer–Vietoris sequence for derived (co)limits under some additional hypotheses, extending the well-known case of a pushout square of group monomorphisms.  相似文献   

6.
James Gillespie 《代数通讯》2017,45(6):2520-2545
A natural generalization of locally noetherian and locally coherent categories leads us to define locally type FP categories. They include not just all categories of modules over a ring, but also the category of sheaves over any concentrated scheme. In this setting we generalize and study the absolutely clean objects recently introduced in [5 Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring (arXiv:1405.5768). [Google Scholar]]. We show that 𝒟(𝒜𝒞), the derived category of absolutely clean objects, is always compactly generated and that it is embedded in K(Inj), the chain homotopy category of injectives, as a full subcategory containing the DG-injectives. Assuming the ground category 𝒢 has a set of generators satisfying a certain vanishing property, we also show that there is a recollement relating 𝒟(𝒜𝒞) to the (also compactly generated) derived category 𝒟(𝒢). Finally, we generalize the Gorenstein AC-injectives of [5 Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring (arXiv:1405.5768). [Google Scholar]], showing that they are the fibrant objects of a cofibrantly generated model structure on 𝒢.  相似文献   

7.
The aim of this paper is an investigation of directed t-packings and in particular of directed t-Steiner systems. A new upper bound on the number of points k for directed t-Steiner systems T(t,k,k) is obtained. We disprove a conjecture of Levenshtein on T(t,k,k) for t 3 by showing that a T(4,6,6) exists. Furthermore, it is proved that the symmetric group S 6 can be partitioned into 30 disjoint T(4,6,6)s. Extensive computer search shows that the tight upper bound on K for t =4,5 is 6 and for t=6 is 7. The non-existence of further small directed t-Steiner systems is established, and large directed t-packings for t,4,5,6 are constructed.  相似文献   

8.
相对复盖与包络   总被引:3,自引:1,他引:2  
丁南庆  陈建龙 《数学学报》1998,41(3):609-616
本文旨在给出相对复盖与包络的特征刻划.作为应用,证明了:若R为任意环,0ABC0为左R 模正合列并且A与C都有平坦复盖,则B有平坦复盖.  相似文献   

9.
关于L内射覆盖   总被引:2,自引:0,他引:2  
周德旭 《东北数学》2004,20(2):207-216
We use the class of L-injective modules to define L-injective covers, and provide the characterizations of L-injective covers by the properties of kernels of homomorphisms. We prove that the right L-noetherian right L-hereditary ring is just such that every right R-module has an L-injective cover which is monic. We also use kernels of homomorphisms to investigate L-simple L-injective covers and give some constructions of L-simple L-injective covers.  相似文献   

10.
Using categorical techniques we obtain some results on localization and colocalization theory in Grothendieck categories with a set of small projective generators. In particular, we give a sufficient condition for such category to be semiartinian. For semiartinian Grothendieck categories where every simple object has a projective cover, we obtain that every localizing subcategory is a TTF-class. In addition, some applications to semiperfect categories are obtained.  相似文献   

11.
本文证明了左n-角范畴的稳定化范畴具有n-角结构,并证明了当n为奇数时,左n-角范畴的Grothendieck群与其稳定化范畴的Grothendieck群同构.  相似文献   

12.
一类局部定向完备集及其范畴的性质   总被引:4,自引:0,他引:4  
管雪冲  王戈平 《数学进展》2005,34(6):677-682
本文给出了局部定向完备集的概念及其在此结构下的一种新的双小于关系,从而进一步给出了一种新的连续性概念,接着讨论了局部定向完备集,连续的局部定向完备集等对象的一些性质,最后考察了三种范畴的笛卡儿闭性,并证明了范畴LDCPO是范畴ALG的反射满子范畴.  相似文献   

13.
A collection of spanning subgraphs of Kn is called an orthogonal double cover if (i) every edge of Kn belongs to exactly two of the Gis and (ii) any two distinct Gis intersect in exactly one edge. Chung and West [3] conjectured that there exists an orthogonal double cover of Kn for all n, in which each Gi has maximum degree 2, and proved this result for n in six of the residue classes modulo 12. In [6], Gronau, Mullin and Schellenberg solved the conjecture. In addition to solving the conjecture, they went on to consider a problem for n 5 mod 6 such that each spanning subgraph Gi consists of the vertex-disjoint union of an isolated vertex, a quadrilateral, and triangles. They proved that for any n 2 mod 3 and n {8, 11, 38, 41, 44, 47, 50, 53, 59, 62, 71, 83, 86, 89, 95, 101, 107, 113, 122, 131, 143, 146, 149, 158, 164, 167, 173, 176, 179, 218, 242, 248, 287}, there exists a quad-rooted double cover of order n. In this note, we improve their result by showing that such designs exist for any n 2 mod 3 and n {8, 11, 38, 41, 44, 50, 53, 62, 71}.  相似文献   

14.
From a representation of a category in terms of a class of Grothendieck categories, a canonical topologisation of the objects follows. The noncommutative topology recently introduced in noncommutative geometry is an example of this. Basic results of sheaf theory are derived in this setting.  相似文献   

15.
徐爱军  王戈平 《数学进展》2006,35(4):485-492
本文引入了代数的局部完备集,FS-局部dcpo,局部稳定映射等概念.主要结果是:以局部Scott连续映射为态射的代数的局部完备集范畴,以局部稳定映射为态射的代数的局部完备集范畴以及以局部Scott连续映射为态射的FS-局部dcpo范畴都是笛卡儿闭范畴.  相似文献   

16.
唐帅 《数学学报》2020,(3):245-252
二面体群的表示范畴为对称半单monoidal范畴,因而其Grothendieck环为有限多个元素生成的交换环.本文确定了该Grothendieck环的极小生成元,并且进一步证明了该Grothendieck环与某一多项式环的商环同构.  相似文献   

17.
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely generated Grothendieck categories. Applications are given for categories of comodules over a coalgebra and for categories of graded modules, and a link to the theory of generalized inverses of matrices is presented. Some of the techniques we use are new, since dealing with arbitrary categories allows us to pass to the dual category.   相似文献   

18.
二面体群的Grothendieck环结构   总被引:1,自引:0,他引:1  
唐帅 《数学学报》1936,63(3):245-252
二面体群的表示范畴为对称半单monoidal范畴,因而其Grothendieck环为有限多个元素生成的交换环.本文确定了该Grothendieck环的极小生成元,并且进一步证明了该Grothendieck环与某一多项式环的商环同构.  相似文献   

19.
20.
Kaivan Ahmadi 《代数通讯》2017,45(7):2848-2854
Let 𝒜 be a Grothendieck category. In this paper we define attached atoms of nonzero objects of 𝒜 as a dual of the associated atoms of nonzero objects introduced by Kanda [2 Kanda, R. (2012). Classifying Serre subcategories via atom spectrum. Adv. Math. 231(3–4):15721588. [Google Scholar]]. If R is a (non)commutative ring, then we show that this new notion can be corresponded to the attached prime ideals of nonzero modules introduced by Macdonald [5 Macdonald, I. G. (1973). Secondary representation of modules over a commutative ring. Sympos. Math. 11:2343. [Google Scholar]] and Annin [1 Annin, S. (2008). Attached primes over noncommutative rings. J. Pure Appl. Algebra 212:510521.[Crossref], [Web of Science ®] [Google Scholar]].  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号