余拟三角双单子

给出了余卷积、余中心元、余扭元、余拟三角双单子的定义,并在单子T的线性型和T-模范畴的辫子之间及单子T的余扭元和T-模范畴的扭元之间建立了双射.     

张量余单子与张量范畴

设是一个张量范畴,g和F均为上的张量余单子,p是一个余单子分配率.本文从FG的张量余单子结构和2-范畴的角度,描述了双余模范畴的张量结构,并给出了其做成张量范畴的一些充要条件. ’     

模糊理论与Kleisli范畴

运用范畴论的观点和语言,讨论了几种真值集不同的模糊集,得出它们都是特殊的模糊理论.更进一步,指出了模糊理论所对应的范畴与由模糊理论诱导的单子所构造的Kleisli范畴的等价关系.最后,通过一个实例,描述了伴随函子诱导的单子,并构造了相应的Kleisli范畴,指出了Kleisli范畴在模糊理论中的应用.     

单子和余单子的缠绕结构

研究单子和余单子的缠绕结构和缠绕模以及与代数和余代数的缠绕结构和缠绕模之间的关系,定义了余单子的类群元,得到了一些有意义的结论.最后构造了缠绕模范畴上的两个函子,并证明了它们是伴随函子.     

超理想的单子及其应用

在扩大模型下,用超理想的单子对超理想进行刻画;进而用它给出了理想为超理想的条件;最后给出理想的单子与超理想的单子之间的关系.     

张量余单子的余半单性与余辫子结构

本文研究了张量余单子的余半单性和余表示范畴,给出了其余半单性和余可裂性的等价性定理.并证明了其余表示范畴是辫子范畴当且仅当该张量余单子是余辫子的.作为应用研究了张量型Hom-双代教的Hom-余模范畴的半单性和辫子结构.     

模糊拓扑空间中Moore-Smith收敛性的非标准刻画

应用了公理化非标准分析理论,将经典集合X上的模糊集扩张成*X上的模糊集.在非标准扩大模型中,定义了模糊邻近结构的单子,并讨论了这些单子的性质及其之间的关系.利用这些单子,刻画了模糊拓扑空间中模糊网的收敛性,进而得到了模糊拓扑空间中Moore-Smith收敛理论的非标准刻画.     

T-余单子可分的等价条件

文章类似于A-上环(coring)给出T-余单子(comonad)的一些性质(这里A是代数,T是单子(monad)).首先定义了实(firm)单子等相关概念,其次研究了与Frobenius函子等价的两个命题,最后给出了与余单子可分等价的五个命题.     

模糊拓扑空间中的单子及其逼近原理

在k-饱和的非标准模型下,以自然的方式定义了模糊拓扑空间中的N-单子,Q-单子和R-单子,并证明了它们相应的逼近原理,讨论了它们之间的相互关系.     

一致结构的单子及其应用

讨论了乘积一致结构的单子的刻画 .利用一致结构的单子给出了 Cauchy网及含小集集族的非标准特征 .作为应用给出一致空间几个重要定理的离散化证明 .     

Semisimple Types in GLn

This paper is concerned with the smooth representation theory of the general linear group G=GL(F) of a non-Archimedean local field F. The point is the (explicit) construction of a special series of irreducible representations of compact open subgroups, called semisimple types, and the computation of their Hecke algebras. A given semisimple type determines a Bernstein component of the category of smooth representations of G; that component is then the module category for a tensor product of affine Hecke algebras; every component arises this way. Moreover, all Jacquet functors and parabolic induction functors connecting G with its Levi subgroups are described in terms of standard maps between affine Hecke algebras. These properties of semisimple types depend on their special intertwining properties which in turn imply strong bounds on the support of coefficient functions.     

Yosida Type Representation for Perfect MV-Algebras

In [9] Mundici introduced a categorical equivalence Γ between the category of MV-algebras and the category of abelian ??-groups with strong unit. Using Mundici's functor Γ, in [8] the authors established an equivalence between the category of perfect MV-algebras and the category of abelian ??-groups. Aim of the present paper is to use the above functors to provide Yosida like representations (see [4]) of a large class of MV-algebras. Mathematics Subject Classification: 03G20, 03B50, 06D30, 06F20.     

Automorphism groups of fields

We consider pairs (K,G) of an infinite field K or a formally real field K and a group G and want to find extension fields F of K with automorphism group G. If K is formally real then we also want F to be formally real and G must be right orderable. Besides showing the existence of the desired extension fields F, we are mainly interested in the question about the smallest possible size of such fields. From some combinatorial tools, like Shelah’s Black Box, we inherit jumps in cardinalities of K and F respectively. For this reason we apply different methods in constructing fields F: We use a recent theorem on realizations of group rings as endomorphism rings in the category of free modules with distinguished submodules. Fortunately this theorem remains valid without cardinal jumps. In our main result (Theorem 1) we will show that for a large class of fields the desired result holds for extension fields of equal cardinality. This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag     

Kaplansky classes and derived categories

We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact and semi-separated scheme X. The approach generalizes and simplifies the method used by the author in (Trans Am Math Soc 356(8) 3369–3390, 2004) and (Trans Am Math Soc 358(7), 2855–2874, 2006) to build monoidal model structures on the category of chain complexes of modules over a ring and chain complexes of sheaves over a ringed space. Indeed, much of the paper is dedicated to showing that in any Grothendieck category , any nice enough class of objects induces a model structure on the category Ch() of chain complexes. The main technical requirement on is the existence of a regular cardinal κ such that every object satisfies the following property: Each κ-generated subobject of F is contained in another κ-generated subobject S for which . Such a class is called a Kaplansky class. Kaplansky classes first appeared in Enochs and López-Ramos (Rend Sem Mat Univ Padova 107, 67–79, 2002) in the context of modules over a ring R. We study in detail the connection between Kaplansky classes and model categories. We also find simple conditions to put on which will guarantee that our model structure is monoidal. We will see that in several categories the class of flat objects form such Kaplansky classes, and hence induce monoidal model structures on the associated chain complex categories. We will also see that in any Grothendieck category , the class of all objects is a Kaplansky class which induces the usual (non-monoidal) injective model structure on Ch().     

Compact representations of BL-algebras

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces. Mathematics Subject Classification (2000):08A72, 03G25, 54B40, 06F99, 06D05     

Motivic decomposition of projective homogeneous varieties and the Krull-Schmidt theorem

Given an algebraic group G defined over a (not necessarily algebraically closed) field F and a commutative ring R we associate the subcategory of the category of Chow motives with coefficients in R, that is, the Tate pseudo-abelian closure of the category of motives of projective homogeneous G-varieties. We show that is a symmetric tensor category, i.e., the motive of the product of two projective homogeneous G-varieties is a direct sum of twisted motives of projective homogeneous G-varieties. We also study the problem of uniqueness of a direct sum decomposition of objects in We prove that the Krull--Schmidt theorem holds in many cases.     

AN EQUIVALENCE BETWEEN RING F AND INFINITE MATRIX SUBRING OVER F

In 1974 Fuller characterized the equivalences between certain subcategories of thecategory of modules over a ring and the category of unital modules over a ring with iden-tity.In this paperthe author uses this equivalence to extend the well-known theorem:F≈M_n(F),where F is a ring with identity and M_n(F)is the ring of matrices over F.     

On Homotopy Types of Alexandroff Spaces

We generalise some results of R. E. Stong concerning finite spaces to wider subclasses of Alexandroff spaces. In particular, we characterize pairs of spaces X,Y such that the compact-open topology on C(X,Y) is Alexandroff, give a homotopy type classification of a class of infinite Alexandroff spaces and prove some results concerning cores of locally finite spaces. We also discuss a mistake found in an article of F.G. Arenas. Since the category of T ₀ Alexandroff spaces is equivalent to the category of posets, our results may lead to a deeper understanding of the notion of a core of an infinite poset.     

On Ext-Transfer for Algebraic Groups

This paper builds upon the work of Cline and Donkin to describe explicit equivalences between some categories associated to the category of rational modules for a reductive group G and categories associated to the category of rational modules for a Levi subgroup H. As an application, we establish an Ext-transfer result from rational G-modules to rational H-modules. In case G = GL_n, these results can be illustrated in terms of classical Schur algebras. In that case, we establish another category equivalence, this time between the module category for a Schur algebra and the module category for a union of blocks for a natural quotient of a larger Schur algebra. This category equivalence provides a further Ext-transfer theorem from the original Schur algebra to the larger Schur algebra. This result extends to the category level the decomposition number method of Erdmann. Finally, we indicate (largely without proof) some natural variations to situations involving quantum groups and q-Schur algebras.     

A_2(F)在G_2(F)中的扩群及其泛正规性

域Ｆ上Ａ２型Ｃｈｅｖａｌｌｅｙ群Ａ２（Ｆ）可视为Ｆ上Ｇ２型Ｃｈｅｖａｌｌｅｙ群Ｇ２（Ｆ）的子群．当 Ｆ是特征不为 ２，３的域且 Ｆ＝Ｆ３时，本文给出了 Ａ２（Ｆ）在 Ｇ２（Ｆ）中的所有扩群及其泛正规性．