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31.
Associated with a finite-dimensional algebra of global dimension at most 2, a generalized cluster category was introduced in Amiot (2009) [1]. It was shown to be triangulated, and 2-Calabi–Yau when it is Hom-finite. By definition, the cluster categories of Buan et al. (2006) [4] are a special case. In this paper we show that a large class of 2-Calabi–Yau triangulated categories, including those associated with elements in Coxeter groups from Buan et al. (2009) [7], are triangle equivalent to generalized cluster categories. This was already shown for some special elements in Amiot (2009) [1]. 相似文献
32.
We prove that for q∈C? not a nontrivial root of unity any symmetric invariant 2-cocycle for a completion of Uqg is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uqg and Ug is unique up to coboundary of a central element. As an application we show that the spectral triple we defined in an earlier paper for the q-deformation of a simply connected semisimple compact Lie group G does not depend on any choices up to unitary equivalence. 相似文献
33.
Matthew Robert Ballard 《Advances in Mathematics》2011,(2):895
We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We introduce the notions of pseudo-adjoints and Rouquier functors and study them. As an application of these ideas and results, we extend the reconstruction result of Bondal and Orlov to Gorenstein projective varieties. 相似文献
34.
本文讨论了双单子分配律的表示及其R-矩阵结构.设F和G是给定的双单子,刻画了单子双模范畴,并给出了其为辫子范畴的充要条件,由此构造了量子YangBaxter方程的一组新解系. 相似文献
35.
In this note we study the local projective model structure on presheaves of complexes on a site, that is, we describe its classes of cofibrations, fibrations, and weak equivalences. In particular, we prove that the fibrant objects are those satisfying descent with respect to all hypercovers. We also describe cofibrant and fibrant replacement functors with pleasant properties. 相似文献
36.
Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to category-theoretical entropy. The two entropies are shown to be equal when the ring is regular, and also for the Frobenius endomorphism of a complete local ring of positive characteristic.Furthermore, given a flat morphism of Cohen–Macaulay local rings endowed with compatible endomorphisms of finite length, it is shown that local entropy is “additive”. Finally, over a ring that is a homomorphic image of a regular local ring, a formula for local entropy in terms of an asymptotic partial Euler characteristic is given. 相似文献
37.
Arnaud Duvieusart 《Journal of Pure and Applied Algebra》2021,225(6):106620
We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini). 相似文献
38.
Correlation Functions and Boundary Conditions in Rational Conformal Field Theory and Three-Dimensional Topology 总被引:3,自引:0,他引:3
Giovanni Felder Jürg Fröhlich Jürgen Fuchs Christoph Schweigert 《Compositio Mathematica》2002,131(2):189-238
We give a general construction of correlation functions in rational conformal field theory on a possibly nonorientable surface with boundary in terms of three-dimensional topological field theory. The construction applies to any modular category in the sense of Turaev. It is proved that these correlation functions obey modular invariance and factorization rules. Structure constants are calculated and expressed in terms of the data of the modular category. 相似文献
39.
After investigating all conceivable properties of decidable objects and maps in left exact categories with well-behaved finite sums (‘lextensive categories’), we give a characterization in such categories of decidable morphisms which are (finite) coverings (in an appropriate sense). Finally, we give two applications of this result, to separable algebras and to local homeomorphisms. In both cases it explains categorically the advantage of two well-known notions — strongly separable algebras and local homeomorphisms with path lifting property, respectively. 相似文献
40.
Relating Categorical Semantics for Intuitionistic Linear Logic 总被引:1,自引:0,他引:1
Maria?Emilia?MaiettiEmail author Paola?Maneggia Valeria?de?Paiva Eike?Ritter 《Applied Categorical Structures》2005,13(1):1-36
There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical models are not sufficient to identify the most appropriate class uniquely. We recommend instead to use the notion of internal language when relating a typed calculus to a class of models. After clarifying the internal languages of the categories of models in the literature we relate these models via reflections and coreflections.
Mathematics Subject Classifications (2000) 03G30, 03B15, 18C50, 03B20. 相似文献