超滤函子余代数范畴

研究了超滤函子余代数范畴set_(F_u)的乘积和余积问题.首先构造了集合乘积上的超滤,讨论集合乘积上超滤的存在形式;接着利用超滤函子的性质给出了范畴set_(F_u)的有限乘积以及任意余积构造;最后证明了范畴set_(F_u)的终对象存在.改进了Gumm关于滤子函子的研究结果,深化了相关文献关于超滤函子余代数的研究.     

余代数K—理论（I）：K0群

本文在余代数上建立了相应的Ｋ０群，研究了Ｋ０函子对余代数的作用，得到了Ｋ０（σ）保持单同态的结构定理。文中给出了一系列余代数的Ｋ０群结构，尤其是在余交换的情形下，用Ｋ０群给出了余交换余代数不可约的一个充要条件。     

关于伪紧余代数、余挠对和弦余代数

本文利用箭图和拓扑伪紧空间研究了K-余代数及其表示.定义了域K上的伪紧K-余代数,研究了伪紧K-余代数和K-代数范畴之间的关系,研究了余挠对和余模逼近,描述了余倾斜余挠对.通过有限维的支撑子余代数和基本的路余代数研究了弦余代数.     

R_0-代数的Stone拓扑表示定理

研究R0-代数中极大滤子的结构性质,通过引入有限平方交性质的概念证明了素理想定理;在全体极大滤子之集上引入了Stone拓扑,研究了Stone空间的性质;在R0-代数中引入了Boole-元的概念,证明了R0-代数的Stone拓扑表示定理,即,全体Boole-元作为Boole代数同构于该R0-代数的Stone空间中的全体既开又闭子集构成的Boole代数。Boole代数的Stone拓扑表示定理可作为该表示定理的特例而给出。     

Gorenstein平坦(余挠)维数和Hopf作用（英文）

设H是域k上的有限维Hopf代数,A是左H-模代数.本文研究了Gorenstein平坦(余挠)维数在A-模范畴和A#H-模范畴之间的关系.利用可分函子的性质,证明了(1)设A是右凝聚环,若A#H/A可分且φ:A→A#H是可裂的(A,A)-双模同态,则l.Gwd(A)=l.Gwd(A#H);(2)若A#H/A可分且φ:A→A#H是可裂的(A,A)-双模同态,则l.Gcd(A)=l.Gcd(A#H),推广了斜群环上的结果.     

泛逻辑学中UB代数的（U—Fuzzy）同态定理

引入了UB代数滤子、Fuzzy滤子和商代数的概念,并按照常规方法(经典集合之间的映射)引入了两个UB代数间的U-fuzzy同态的概念,给出了UB代数的同态与同态基本定理和u-fuzzy同态基本定理,在最后引入了fuzzy同态的概念,初步讨论了一些结果.     

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.     

MV-代数的素滤子MV-拓扑空间

在MV-方体[0,1]X的子集Ω上引进MV-拓扑结构,并套论MV-拓扑空间的紧性、Hausdorff分离性等拓扑性质.细致地讨论MV-代数的素滤子集上的MV-拓扑空间(M,ΩM),证明素滤子MV-拓扑空间是紧Hausdorff MV-空间,并且它还是良紧空间.作为应用,证明一个σ-完备格M是MV-代数当且仅当M同构于某个Stone MV-空间的MV-开闭集格.     

格蕴涵代数上的同余关系

本文研究格蕴涵代数上的同余关系，给出了同余关系诱导的商格蕴涵代数，格蕴涵同态诱导的同命关系，滤子与同余关系之间的联系．     

格蕴涵代数的左幂等元

为了研究命题真值取于格上的逻辑系统,文献[1]给出了格蕴涵供数的概念,文献[2-6]给出了格蕴涵代数的滤子,同态和性质（P）的概念,并讨论了它们的一些性质。本文在格蕴函代数中引入左幂等元的概念,讨论格蕴函代数中左幂等元的性质及由全体左幂等元所构成集合的代数结构,得到格蕴涵代数的分解定理：格蕴涵代数可以分解为由左幂等元构成左映射的像集合与对偶核的直和。     

廣義Stieltjes-Post反演公式及漸近積分

<正> 在作者之一的文章[1]中,曾定義過一種含有参數的正規變換函數類。對於以這類中的函數為核所構成的積分變換,即存在有一種廣義的Stieltjes-Post-Widder反演公式。在本文的第一節中,我們將對正規變換函數定義中的第二條件予以减弱,也就是把核函數的範圍加以放寬,而仍保持廣義反演公式的有效.在本文的第二節中,主要是改善先前一篇短文[2]中的結果,我們將在較廣泛的條件下,重新建立某一漸近積分定理.     

拟Abelian范畴上函子范畴的局部化

通过拟Abelian范畴的局部类构造出函子范畴的局部类,进一步研究函子范畴的局部化范畴与局部化范畴的函子范畴之间的关系.     

Tambara Functors on Profinite Groups and Generalized Burnside Functors

The Tambara functor was defined by Tambara in the name of TNR-functor, to treat certain ring-valued Mackey functors on a finite group. Recently Brun revealed the importance of Tambara functors in the Witt–Burnside construction. In this article, we define the Tambara functor on the Mackey system of Bley and Boltje. Yoshida's generalized Burnside ring functor is the first example. Consequently, we can consider a Tambara functor on any profinite group. In relation with the Witt–Burnside construction, we can give a Tambara-functor structure on Elliott's functor V _M , which generalizes the completed Burnside ring functor of Dress and Siebeneicher.     

Tambarization of a Mackey functor and its application to the Witt–Burnside construction

For an arbitrary group G, a (semi-)Mackey functor is a pair of covariant and contravariant functors from the category of G-sets, and is regarded as a G-bivariant analog of a commutative (semi-)group. In this view, a G-bivariant analog of a (semi-)ring should be a (semi-)Tambara functor. A Tambara functor is firstly defined by Tambara, which he called a TNR-functor, when G is finite. As shown by Brun, a Tambara functor plays a natural role in the Witt–Burnside construction.It will be a natural question if there exist sufficiently many examples of Tambara functors, compared to the wide range of Mackey functors. In the first part of this article, we give a general construction of a Tambara functor from any Mackey functor, on an arbitrary group G. In fact, we construct a functor from the category of semi-Mackey functors to the category of Tambara functors. This functor gives a left adjoint to the forgetful functor, and can be regarded as a G-bivariant analog of the monoid-ring functor.In the latter part, when G is finite, we investigate relations with other Mackey-functorial constructions — crossed Burnside ring, Elliott?s ring of G-strings, Jacobson?s F-Burnside ring — all these lead to the study of the Witt–Burnside construction.     

AF-algebras and topology of mapping tori

The paper studies applications of C*-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4. In conclusion, we consider two numerical examples illustrating our main results.     

A note on coinduction functors between categories of comodules for corings

In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case oflocally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a moregeneral coinduction functor between categories of type σ[M]. In special cases (e.g. the corings morphism is part of a morphism of measuringa-pairings or the corings have the same base ring), a version of our functor is shown to be isomorphic to the usual coinduction functor obtained by means of the cotensor product. Our results in this note generalize previous results of the author on coinduction functors between categories of comodules for coalgebras over commutative base rings.     

Monads generated by monoids

In this note we consider monoids in and (tensored) monadson a monoidal categoryV. We prove the canonical inclusion functor from the category of monoids inV to the category of monads onV to be coadjoint. Furthermore, we show that this adjunction is induced by a monoidal adjunction. We characterize the monads generated by monoids (by means of the inclusion functor).Finally we consider an application to commutative monads (and monoids) and discuss possible generalizations. Some parts of our results have been obtained by M.C. Bunge and H. Wolff in the case of a symmetric monoidal closed category.     

On the fractions of semi-Mackey and Tambara functors

For a finite group G, a semi-Mackey (resp. Tambara) functor is regarded as a G-bivariant analog of a commutative monoid (resp. ring). As such, some naive algebraic constructions are generalized to this G-bivariant setting. In this article, as a G-bivariant analog of the fraction of a ring, we consider fraction of a Tambara (and a semi-Mackey) functor, by a multiplicative semi-Mackey subfunctor.