Digital Cofibration and Digital Lusternik-Schnirelmann Category in the Sense of Subdivision

In this paper, using the notion of subdivision, the authors generalize the definition of cofibration in digital topology and show that this kind of cofibration is injective in the sense of subdivision. Meanwhile, they give the necessary condition under which a digital map is a cofibration. Furthermore, they consider the Lusternik-Schnirelmann category of digital maps in the sense of subdivision and give several fundamental homotopy properties about it.     

The double Ringel-Hall algebra on a hereditary abelian finitary length category

In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of H (ρ) and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.     

Stone's representation theorem in fuzzy topology

In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.     

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 the Buchstaber Invariant of Simple Convex 3-Polytopes

In this paper the author gives a method of constructing characteristic matrices,and uses it to determine the Buchstaber invariants of all simple convex 3-polytopes,which imply that each simple convex 3-polytope admits a characteristic function.As a further application of the method,the author also gives a simple new proof of five-color theorem.     

A Parameterization of the Canonical Bases of Affine Modified Quantized Enveloping Algebras

For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T~2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U~+.     

余拟三角弱Hopf群代数与辫子Monoidal范畴

In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β: Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ.     

畴数理论在纤维空间的应用

In this paper, we improve a result of James′ paper [1], and get the theorem; If P:E→B is a fibration, B is a normal space, and catB= n, then the composition of n filre-trivial maps is section homolopic.     

Sober拓扑分子格

A topological molecular lattice (TML) is a pair (L, T), where L is a completely distributive lattice and r is a subframe of L. There is an obvious forgetful functor from the category TML of TML‘s to the category Loc of locales. In this note,it is showed that this forgetful functor has a right adjoint. Then, by this adjunction,a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.     

广义直觉模糊集的范畴

In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS axe studied. Firstly， it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers， Secondly， it is proved that the category GIFS has middle object and consequently GIFS is a weak topos.Thirdly， by the use of theory of weak topos GIFS，the power object of an object in GIFS is studied.     

一般化凸空间上的一个连续选择定理(英文)

本文研究一般化凸空间上的连续选择定理.利用在D■X的条件下,一般化凸空间(X,D;Γ)上Γ-凸子集的概念,得到了两类一般化凸空间之间,以及φ映射和Γ-凸映射之间的关系,并且得到了一个连续选择定理.本文推广了一般化凸空间上凸子集的概念.     

Fuzzy subobjects in a category and the theory of C-sets

In this paper we shall define the concept of a fuzzy subobject of an object in arbitrary categories. This concept is generated by the representation theorem of fuzzy sets. By using fuzzy subobjects one can include most of the fuzzy concepts defined in the literature, such as: fuzzy groups, fuzzy relations and fuzzy convex sets. In the second part of the paper we shall define a new concept; that of a $\text{C}$-set. This concept will generalize that of a fuzzy set and we shall also prove that $\text{C}$-sets can be represented by some sets of functors. More precisely, $\text{C}$-sets form a category which can be represented by a category of functors. The utility of $\text{C}$-sets resides in the fact that one can replace “ordering” by the more general concept of a morphism in category. The new representation of $\text{C}$-sets is weaker than that of fuzzy sets.     

完全■-单半群

完全■-单半群是完全单半群和完全■~*-单半群在U-半富足半群类中的一个自然推广.本文证明了半群S是完全■-单半群,当且仅当S同构于幺半群T上的正规Rees矩阵半群■(T;I,A;P).这一结果不仅推广了完全单半群的著名Rees定理,而且推广了任学明和岑嘉评在2004年建立的完全■~*-单半群的一个结构定理.     

Simple free star-autonomous categories and full coherence

This paper gives a simple presentation of the free star-autonomous category over a category, based on Eilenberg–Kelly–MacLane graphs and Trimble rewiring, yielding a full coherence theorem: the commutativity of diagrams of canonical maps is decidable.     

Local analytic reduction of families of diffeomorphisms

We study local analytic simplification of families of analytic maps near a hyperbolic fixed point. A particularly important application of the main result concerns families of hyperbolic saddles, where Siegel's theorem is too fragile, at least in the analytic category. By relaxing on the formal normal form we obtain analytic conjugacies. Since we consider families, it is more convenient to state some results for analytic maps on a Banach space; this gives no extra complications. As an example we treat a family passing through a 1:−1 resonant saddle.     

κ-线性双扩张范畴(Ⅰ)

κ-线性范畴是有限维κ-代数的自然推广.对应于双扩张代数,定义了κ-线性双扩张范畴■,并且证明了■Mod等价于四元组范畴■,推广了双扩张代数的模范畴理论.     

半群S-分次环与冲积R#S~*

设S为任意半群,本文以S-集为基础,讨论了S-集分次模的一些性质并得到范畴(S,A,R)-gr的一个有限生成投射生成子集合;对于冲积R#S*,主要证明了在一定条件下, unital左R#S*-模范畴和分次R-模范畴是同构的.     

平衡范畴与半群的双序

研究范畴与半群通过幂等元双序建立的一种自然联系.对每个有幂等元的半群S,其幂等元生成的左、右主理想之集通过双序ω~e,ω~r自然确定两个有子对象、有像且每个包含都右可裂的范畴L(S),R(S),其中态射的性质与S中元素的富足性、正则性有自然对应.利用这个联系,我们定义了"平衡(富足、正规)范畴"概念.对任一平衡(富足、正规)范畴■,我们构造其"锥半群"■,证明■左富足(富足、正则),且每个平衡(富足、正规)范畴■都与某左富足(富足、正则)半群S的左主理想范畴L(S)(作为有子对象的范畴)同构.     

高维空间中的有界凸域

证明n维空间中的有界凸域D能被拟共形映射到n维单位球B~n(0,1),即D是拟球,从而说明拟共形映射中的黎曼定理在n维空间中的有界凸域类中是成立的．     

Holomorphe Korrespondenzen und Meromorphe Abbildungen Allgemeiner Komplexer Räume-Fortsetzungssätze

The numerous results concerning analytic sheaf extension obtained in the last time can be applied to the extension problem for holomorphic correspondences and meromorphic mappings of complex spaces. In this paper, from a fundamental theorem of J. Frisch and J. Guenot [3, Th. VII. 2] extension theorems of the type of the 2^nd Riemann removable singularities theorem are deduced.The definition of holomorphic correspondences is based on a categorial concept; it is shown that an arbitrary category with products and fibre products can be embedded in a category of correspondences.