共查询到19条相似文献,搜索用时 62 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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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. 相似文献
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尹翠 《数学年刊A辑(中文版)》1997,(4)
本文建立了函子范畴等价的Morita理论.考虑的主要问题是modC何时等价于modC′及这些等价条件.同时定义了函子范畴的双模和函子张量积,并刻画了等价函子. 相似文献
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左模张量积函子Ⅰ 总被引:1,自引:1,他引:0
设K={0,1,α,β,…}是一个有么元可换环,R={0,1,γ_1 γ_2,…}与S={0,1,s_1 S_2,…}均为K-环。A={0,α_1,α_2,…}是左酉R-模,C={o,c_1,c_2,…}是左酉S-模。在文献[1]中,周伯壎教授定义了A与C的左模张量积AC,它是一个左RS-模。本文中的K、R、S、A、C均如上定义;除非有特别的声明,模均表示左模;如环有么元,模就表示左酉模。 在文献中,有古典张量积(Kronecker product)的定义:如R是一环,A∈,C∈_R,则AC是一个加群,它既不是左R-模,也不是右R-模。此后,左模张量积记为,而古典张量积记为。 相似文献
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Hiroyuki Nakaoka 《代数通讯》2013,41(9):3095-3151
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. 相似文献
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H. Peter Gumm 《Algebra Universalis》2001,45(2-3):135-147
Functors preserving weak pullbacks provide the basis for a rich structure theory of coalgebras. We give an easy to use criterion
to check whether a functor preserves weak pullbacks. We apply the characterization to the functor which associates a set X with the set (X) of all filters on X. It turns out that this functor preserves weak pullbacks, yet does not preserve weak generalized pullbacks. Since topological
spaces can be considered as -coalgebras, in fact they constitute a covariety, we find that the intersection of subcoalgebras need not be a coalgebra,
and 1-generated -coalgebras need not exist.
Received August 24, 1998; accepted in final form October 12, 1998. 相似文献
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Let 𝒞 be an arbitrary category. We study strongly involutory functors on 𝒞, defined as involutory contravariant endofunctors of 𝒞 acting as identity on objects. Motivating examples can be constructed if we think at the transpose of a matrix, the adjoint of a linear continuous operator between two Hilbert spaces, and the inverse of a morphism in a groupoid. We show how a strongly involutory functor on a skeleton of 𝒞 extends to 𝒞, and we apply this to find all such functors for a groupoid. We describe and classify up to a natural equivalence all strongly involutory functors on the category of finite dimensional vector spaces over a field. Strongly involutory functors with a special property related to generalized inverses of morphisms are studied. 相似文献
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Yolanda Moreno 《Applied Categorical Structures》2008,16(5):617-627
We obtain new categorical proofs that generalize the diagonal principles introduced in Castillo and Moreno (Israel J. Math.
140:253–270, 2004) to study the automorphic and partially automorphic character of Banach spaces. We then introduce and study the automorphy
index for a Banach space, showing that while .
This research has been supported in part by project MTM2004-02635. 相似文献
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Hiroyuki Nakaoka 《代数通讯》2013,41(12):5105-5148
In this article, we will show that the category of biset functors can be regarded as a reflective monoidal subcategory of the category of Mackey functors on the 2-category of finite groupoids. This reflective subcategory is equivalent to the category of modules over the Burnside functor. As a consequence of the reflectivity, we can associate a biset functor to any derivator on the 2-category of finite categories. 相似文献
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In the context of Mackey functors we introduce a category whichis analogous to the category of modules for a quasi-hereditaryalgebra which have a filtration by standard objects. Many ofthe constructions which work for quasi-hereditary algebras canbe done in this new context. In particular, we construct ananalogue of the Ringel dual, which turns out hereto be a standardly stratified algebra. The Mackey functors whichplay the role of the standard objects are constructed in thesame way as functors which have been used previously in parametrizingthe simple Mackey functors, but instead of using simple modulesin their construction (as was done before) we use p-permutationmodules. These Mackey functors are obtained as adjoints of theoperations of forming the Brauer quotient and its dual. Thefiltrations which have these Mackey functors as their factorsare closely related to the filtrations whose terms are the sumof induction maps from specified subgroups, or are the commonkernel of restriction maps to these subgroups. These latterfiltrations appear in Conlon's decomposition theorems for theGreen ring, as well as in other places, where they arise quitenaturally. 2000 Mathematics Subject Classification: primary 20C20; secondary20J05, 19A22, 16G70, 16E60. 相似文献
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