共查询到20条相似文献,搜索用时 15 毫秒
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研究函子范畴ModC上加性函子的表示,把一个Abel群作成范畴ModC上的一个左C-模,构造出一个Hom函子和一个函子态射,证明了从函子范畴ModC到范畴Ab的任意变和为积的反变左正合可加函子都与某个Hom函子自然等价.所得结论在函子范畴上,推广了Watts定理. 相似文献
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黄文平 《纯粹数学与应用数学》1994,10(1):45-48
本文给出了交换环上的四元数环是除的两个充要条件,在环范畴的子范畴间定义子四元数函数子,并证明了它是一个正合函子,同时讨论了环类的遗传性,同态闭性在四元数函子下的变化情况。 相似文献
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本文研究了环上模范畴与余环上余模范畴.运用可裂叉与余可分余环的性质,得到了以上两个范畴等价的一些充分条件,从而推广了文献[6]中的一些结果.Abstract: In this article,we consider the categories of modules over rings and categories of comodules over corings.By properties of split forks and coseparable corings,we get some sufficient conditions for the equivalence between above two categories.As a consequence,we generalize some results in[6]. 相似文献
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《Quaestiones Mathematicae》2013,36(3):323-337
Abstract It is shown that the category CS of closure spaces is a topological category. For each epireflective subcategory A of a topological category X a functor F A :X → X is defined and used to extend to the general case of topological categories some results given in [4], [5] and [10] for epireflective subcategories of the category Top of topological spaces. 相似文献
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设 G是有限群 ,R是强 G-分次环 .本文证明了 R Re-与 Hom Re(R,- )都是从模范畴 R - mod到 Re- mod的“纯量”限制函子 F的伴随函子 ,并且两个函子 R Re-和Hom Re(R,- )是自然同构的 . 相似文献
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《Quaestiones Mathematicae》2013,36(1-3):227-254
Abstract Generalizing results of Herrlich and Nel, the author characterizes by means of smallest proper structures those objects X of an initially structured category for which X x—has a right adjoint, and describes the corresponding function spaces. It is shown that reduction to finally and initially dense classes is possible. The results are applied to epireflective subcategories of the category of limit spaces containing a finite non-indiscrete space, in particular to epireflective subcategories of TOP. 相似文献
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扩展de Bruijn图EB(d,m;h1,h2,…,hk)是de Bruijn图的一种推广,它是一种再要的网络互连结构.本文主要研究扩展de Bruijn图中的有根生成树,证明了对任何顶点u和任意整数r:2≤r≤d,扩展de Bruijn图都有以u为根且深度为[log(?),d]·max{hi:1≤i≤k}的rk-叉生成树,并由此获得了扩展de Bruijn图的广播时间的上界. 相似文献
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《Quaestiones Mathematicae》2013,36(1):71-81
Abstract The concept of a T-discrete object is a generalization of the notion of discrete spaces in concrete categories. In this paper. T-discrete objects are used to define discrete functors. Characterizations of discrete functors are given and their relation to other important functors are studied. A faithful functor T: A → X is discrete iff the full subcategory B of A consisting of all T-discrete objects is (X-iso)-coreflective in A. It follows that the existence of bicoreflective subcategories is equivalent to the existence of suitable discrete functors. Finally, necessary and sufficient conditions are found such that for a given functor T: A → X, the full subcategory B of A consisting of all T-discrete A-objects is monocoreflective in A. 相似文献
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We define symmetric and exterior powers of categories, fitting into categorified Koszul complexes. We discuss examples and calculate the effect of these power operations on the categorical characters of matrix 2-representations. 相似文献
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《Quaestiones Mathematicae》2013,36(2):129-136
Abstract Nilpotent and solvable ideals are defined and investigated in categories. The relation between the prime radical and the sum of the solvable ideals (which is also a radical) is discussed in categories. For example: If an object satisfies the maximal condition for ideals, then the prime radical is equal to the sum of the solvable ideals. Certain generalizations of theorems in rings, groups, Lie algebras, etc. are also proven, for example: An ideal α: I → A is semiprime if and only if A/I contains no non-zero nilpotent ideals. 相似文献
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《Quaestiones Mathematicae》2013,36(2):121-158
Abstract The well known characterizations of equational classes of algebras with not necessaryly finitary operations by FELSCHER [6.7] and of categories of A-algebras for algebraic theories A in the sense of LINTON [10], esp., by means of their forgetful functors are the foundations of a concept of varietal functors U:K → L over arbitrary basecategories L. They prove to be monadic functors which satisfy an additional HOM-condition [17]. (In the case L = Set this condition is always fulfilled, see LINTON [11].) Contrary to monadic functors, varietal functors are closed under composition. Pleasent algebraic properties of the base-category L can be ‘lifted’ along varietal functors, such as e.g. factorization properties, (co-) completeness, classical isomorphism theorems, etc. By means of the well known EILENBERG-MOORE-algebras there is a universal monadic functor UT:L T → L for any functor U: K → L, having a left adjoint F (T: = UF). But, in general, UT is not varietal. Under some suitable conditions, however it is possible, to construct a canonical varietal functor ?:R → L, the varietal hull of U. This hull has much more interesting (algebraic) properties than the EILENBERG-MOORE construction. Moreover, results of BANASCHEWSKI-HERRLICH [2] are extended. 相似文献
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本文构造了在完备格上模糊集范畴.利用极小扩展原则和范畴的性质,获得了函子Uα构成集合范畴上的模结构,推广了P.Eklund的结论. 相似文献
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《Quaestiones Mathematicae》2013,36(1-4):149-206
Abstract A standard extension (resp. standard completion) is a function Z assigning to each poset P a (closure) system ZP of subsets such that x ? y iff x belongs to every Z ε ZP with y ε Z. A poset P is Z -complete if each Z ε 2P has a join in P. A map f: P → P′ is Z—continuous if f?1 [Z′] ε ZP for all Z′ ε ZP′, and a Z—morphism if, in addition, for all Z ε ZP there is a least Z′ ε ZP′ with f[Z] ? Z′. The standard extension Z is compositive if every map f: P → P′ with {x ε P: f(x) ? y′} ε ZP for all y′ ε P′ is Z -continuous. We show that any compositive standard extension Z is the object part of a reflector from IPZ, the category of posets and Z -morphisms, to IRZ, the category of Z -complete posets and residuated maps. In case of a standard completion Z, every Z -continuous map is a Z -morphism, and IR2 is simply the category of complete lattices and join—preserving maps. Defining in a suitable way so-called Z -embeddings and morphisms between them, we obtain for arbitrary standard extensions Z an adjunction between IPZ and the category of Z -embeddings. Many related adjunctions, equivalences and dualities are studied and compared with each other. Suitable specializations of the function 2 provide a broad spectrum of old and new applications. 相似文献