自由函子及其伴随函子

本文证明了由集合范畴到f-模范畴的自由函子的存在性，构造了自由函子的伴随函子。     

The Homomorphism Lattice Induced by a Finite Algebra

Each finite algebra A induces a lattice L _A via the quasi-order → on the finite members of the variety generated by A, where B →C if there exists a homomorphism from B to C. In this paper, we introduce the question: ‘Which lattices arise as the homomorphism lattice L _A induced by a finite algebra A?’ Our main result is that each finite distributive lattice arises as L _Q , for some quasi-primal algebra Q. We also obtain representations of some other classes of lattices as homomorphism lattices, including all finite partition lattices, all finite subspace lattices and all lattices of the form L ⊕1, where L is an interval in the subgroup lattice of a finite group.     

HX环的同态

文[1]首先建立了HX环的概念,将环上的代数结构自然地引导出它的幂集上的某种代数结构。类似的问题是：环的同态能否诱导出它们的HX环之间的同态?本文较详细地讨论HX环的同态。     

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.     

L—Fuzzy群的同志和同构

本文研究了Ｌ—Ｆｕｚｚｙ群的同态和同构，给出了它们的一些性质，并把群论中的同态定理和同构定理推广到Ｌ—Ｆｕｚｚｙ群上     

The Homomorphism and Isomorphism on Hypergroup

61.IntroductionThispapersupposesthatthe(G,')isagroup,inP,(G)HP(G)-{di},itisstiuplatedtheoperationasthefollowing:A.BH{a.blaeA,beB}.(1.1)ThenP,(G)isasemigroup.Iftheunempty@=P,(G)makesupagroupwith(1.l),then@iscalledthehypergroupofG,here'E'standsfortheunitelement,especially,wheneeEinG,wecallgasareguIarhypergroup,whencontraryelementsandcontrarysetsof@conformedtoeachother,wecallopasauniformhypergroup.Obviously,Eisasemi-subgroupofG.Whengisregular,Eisasemi-subgroupwithunitelement,When@isunif…     

Flows With Respect to a Functor

Flows with respect to a functor F are introduced as a common generalization of the concepts of F-co-structured sinks and small F-co-structured sources. Appropriate factorization structures for functors are investigated and used to obtain several results that characterize coadjoint functors that have domains with various completeness conditions. When the functor in question is an identity functor, these results reduce to earlier results of Herrlich and Meyer for flows in a category. Functors of the type in question are shown to be nicely behaved with respect to composition. The dual notion of wolfs with respect to a functor is introduced, as is the concept of (co)limit with respect to a functor.     

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.     

The Real Spectrum of a Noncommutative Ring and the Artin-Lang Homomorphism Theorem

Let R be a noncommutative ring. Two epimorphisms

$$\alpha_{i}:R\to (D_{i},\leqslant_{i}),\quad i = 1,2 $$

from R to totally ordered division rings are called equivalent if there exists an order-preserving isomorphism ? : (D ₁, ? ₁) → (D ₂, ? ₂) satisfying ? ° α ₁ = α ₂. In this paper we study the real epi-spectrum of R, defined to be the set of all equivalence classes (with respect to this relation) of epimorphisms from R to ordered division rings. We show that it is a spectral space when endowed with a natural topology and prove a variant of the Artin-Lang homomorphism theorem for finitely generated tensor algebras over real closed division rings.

     

The Functor of Order-Preserving Functionals of Finite Degree

It is proved that the space of all order-preserving functionals with finite supports is a compact, and if the supports are one-point sets, then this space is the Stone-Chech compactification of a given Tychonoff space. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 313, 2004, pp. 135–138.     

函子范畴的Recollement

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．     

Closure Operators with Respect to a Functor

A notion of closure operator with respect to a functor U is introduced. This allows us to describe a number of mathematical constructions that could not be described by means of the already existing notion of closure operator. Some basic results and examples are provided.     

集合范畴上超滤函子的余代数

定义了集合范畴上的超滤函子F_u(-),并研究了相关性质.包括函子F_u(-)在有限集上保拉回,一个集合的子集成为F_u-子余代数的充要条件,以及两个余代数之间的态射是F_u-余代数同态的充要条件,子集成为子余代数的充要条件,最后以拓扑空间作为F_u-余代数的具体实例,研究了拓扑空间的连续映射与超滤函子的余代数同态之间的关系.     

Functor D and strong homotopy

This paper studies functor D and strong homotopy, introduced earlier by the author [1]. A theorem is proven on mappings, and the connection is established between the concepts of strong homotopy of DGA-mapping of coalgebras and functor D. As topological applications, in particular, it is shown that continuous mappings of the sphere f, g: S^2n–1Sⁿ have one and the same Hopf invariant if and only if the induced chain of mappings is strongly homotopic.Translated from Matematicheskie Zametki, Vol. 21, No. 4, pp. 557–564, April, 1977.     

The Structural Nature of the Nerve Functor for n-Groupoids

Given a left exact category B, the construction of the nerve functor _n for n-groupoids in B is related to a certain property of the category S-S i m p l _{n – 1} B of the split (n – 1)-truncated simplicial objects in B, which allows us to define the split n-truncated simplicial objects in B completely internally to S-S i m p l _{n – 1} B and thus to construct intrisincally from it the category S-S i m p l _n B.     

Polynomial Filtrations and Lannes'' T Functor

This paper defines and studies the polynomial filtration [p_k ] of the shift functor : F , where F is the category of functors between F-vector spaces over a finite field F. The functors [p_k ] correspond to a system of functors (p_k T):U U, related to Lannes'T-functor on the category U of unstable modules over the Steenrod algebra. The main results concern the behaviour of the quotients ~ _s:=~/[p_s-1~ filtrations by ~_s-nilpotent functors are introduced and it is shown that the full subcategory of _s-nilpotent functors is thick.     

S-Structures for k-Linear Categories and the Definition of a Modular Functor

Ideas from string theory and quantum field theory have beenthe motivation for new invariants of knots and 3-dimensionalmanifolds which have been constructed from complex algebraicstructures such as Hopf algebras [17, 22], monoidal categorieswith additional structure [24], and modular functors [14, 23].These constructions are closely related. Here we take a unifyingcategorical approach based on a natural 2-dimensional generalisationof a topological field theory in the sense of Atiyah [1], andshow that the axioms defining these complex algebraic structuresare a consequence of the underlying geometry of surfaces.     

Fuzzy子格与Fuzzy同态

每个代数结构一般都可引入相应的Ｆｕｚｚｙ子结构，为了进一步研究Ｆｕｚｚｙ子和以及Ｆｕｚｚｙ同态的各种性质，本文引入了亚格的概念，并建立了Ｆｕｚｚｙ子格与亚格的对应关系（定理１．７）；给出了Ｆｕｚｚｙ同态（同构）的分解定理（定理２．５和推论２．７）；最后讨论了同余关系商格的Ｆｕｚｚｙ子格问题，证明了在自然映射下，任一保序映射可以引导出商格中应的Ｆｕｚｚｙ子格，并由此引出了φ－Ｆｕｚｚｙ商子格的概念。     

The Behaviors of Expansion Functor on Monomial Ideals and Toric Rings

In this article, we study some algebraic and combinatorial behaviors of expansion functor. We show that on monomial ideals some properties like polymatroidalness, weakly polymatroidalness, and having linear quotients are preserved under taking the expansion functor.

The main part of the article is devoted to study of toric ideals associated to the expansion of subsets of monomials which are minimal with respect to divisibility. It is shown that, for a given discrete polymatroid P, if toric ideal of P is generated by double swaps, then toric ideal of any expansion of P has such a property. This result, in a special case, says that White's conjecture is preserved under taking the expansion functor. Finally, the construction of Gröbner bases and some homological properties of toric ideals associated to expansions of subsets of monomials is investigated.