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1.
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
2.
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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4.
Jiří Adámek Horst Herrlich Jiří Rosický Walter Tholen 《Applied Categorical Structures》2002,10(3):237-249
Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey. 相似文献
5.
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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7.
We investigate functors between abelian categories having a left adjoint and a right adjoint that are similar (these functors are called quasi-Frobenius functors). We introduce the notion of a quasi-Frobenius bimodule and give a characterization of these bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of quasi-Frobenius homomorphism of corings is introduced. Finally, a version of the endomorphism ring Theorem for quasi-Frobenius extensions in terms of corings is obtained. 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
10.
Miroslav Doupovec 《Czechoslovak Mathematical Journal》2005,55(4):901-916
For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber
product preserving functors defined on the category of fibered manifolds with m-dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce
the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors.
Tis work was supported by a grant of the GA CR No. 201/02/0225. 相似文献
11.
Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F. 相似文献
12.
Chang Chang XI 《数学学报(英文版)》2006,22(2):625-640
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension. 相似文献
13.
Henning Krause 《Algebras and Representation Theory》2003,6(5):475-499
Given a locally presentable additive category A, we study a class of covariantly finite subcategories which we call definable. A definable subcategory arises from a set of coherent functors F
i
on A by taking all objects X in A such that F
i
X=0 for all i. We give various characterizations of definable subcategories, demonstrating that all covariantly finite subcategories which arise in practice are of this form. This is based on a filtration of the category of all coherent functors on A. 相似文献
14.
Mohammad T. Dibaei 《代数通讯》2013,41(8):3097-3101
15.
Patrik Lundström 《代数通讯》2013,41(8):3029-3041
We show that groupoid rings are separable over their ring of coefficients if and only if the groupoid is finite and the orders of the associated principal groups are invertible in the ring of coefficients. We use this to show that if we are given a finite groupoid, then the associated groupoid ring is semisimple (or hereditary) if and only if the ring of coefficients is semisimple (or hereditary) and the orders of the principal groups are invertible in the ring of coefficients. To this end, we extend parts of the theory of graded rings and modules from the group graded case to the category graded, and, hence, groupoid graded situation. In particular, we show that strongly groupoid graded rings are separable over their principal components if and only if the image of the trace map contains the identity. 相似文献
16.
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
17.
Zhou Caijun 《数学学报(英文版)》1996,12(4):413-414
In this short paper, we prove that ifR is a regular local ring of unequal characteristic, then there exists an additive covariant functorG from the category of abelian sheaves on SpecR to the category of abelian groups such that id
R
(G(R))>dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative. 相似文献
18.
We study the derived functors of Hom that are computed by using flat resolutions of Hom. These are denoted n. We compare these with the usual Extn's and show that 1⊂ Ext1and indicate (using MacLane's terminology) why the class of associated short exact sequences is a proper class. When the ring is a Dedekind domain we classify the N such that n(–, N) = 0 and show that unlike the situation for other classically defined right derived functors of Hom, Hom is not balanced relative to the two classes of modules that make 1 vanish. 相似文献
19.
Yu Liu 《数学学报(英文版)》2019,35(8):1334-1356
In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394, 245–284 (2013)”, we introduced the notion o 相似文献
20.
K.A.Hardie与K.H.Kamps研究过固定空间B上的迹同伦范畴([1]).他们引进了两对伴随函子PB┤NB与m┤m,此处m:AB是固定映射,PB:HBHB与m:HAHB是函子.我们在[2]中引进了分裂的范畴纤维化L:HbHB,并且证明了L┤J,J┤L.本文首先将PB┤NB推广到PBb┤NBb#,其中b:BB是任一固定映射,并且我们还得到涉及迹同伦范畴Hb与Hb的两对伴随函子,此处Hb是Hb的对偶.特别,Nb┤Pb不同于PB┤NB. 相似文献