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91.
Given an algebraic theory
whose category of models is semi-abelian, we study the category
of topological models of
and generalize to it most classical results on topological groups. In particular,
is homological, which includes Barr regularity and forces the Mal'cev property. Every open subalgebra is closed and every quotient map is open. We devote special attention to the Hausdorff, compact, locally compact, connected, totally disconnected and profinite
-algebras. 相似文献
92.
Fang LI Gong Xiang LIU 《数学学报(英文版)》2006,22(4):1027-1046
There are at least two kinds of generalization of Hopf algebra, i.e. pre-Hopf algebra and weak Hopf algebra. Correspondingly, we have two kinds of generalized bialgebras, almost bialgebra and weak bialgebra. Let L = (L, ×, I, a, l, r) be a tensor category. By giving up I, l, r and keeping ×, a in L, the first author got so-called pre-tensor category L = (L, ×, a) and used it to characterize almost bialgebra and pre-Hopf algebra in Comm. in Algebra, 32(2): 397-441 (2004). Our aim in this paper is to generalize tensor category L = (L, ×, I, a, l, r) by weakening the natural isomorphisms l, r, i.e. exchanging the natural isomorphism ll^-1 = rr^-1 = id into regular natural transformations lll= l, rrr = r with some other conditions and get so-called weak tensor category so as to characterize weak bialgebra and weak Hopf algebra. The relations between these generalized (bialgebras) Hopf algebras and two kinds generalized tensor categories will be described by using of diagrams. Moreover, some related concepts and properties about weak tensor category will be discussed. 相似文献
93.
Tetsuya Sato 《Journal of Pure and Applied Algebra》2018,222(10):2888-2896
We show that the Giry monad is not strong with respect to the canonical symmetric monoidal closed structure on the category Meas of all measurable spaces and measurable functions. 相似文献
94.
95.
In this paper, we establish some new Foxby equivalences between some Gorenstein subcategories in the Auslander class 𝒜C(R) and that in the Bass class ?C(S) in a general setting. Our results provide a unification and generalization of some known results and generate some new Foxby equivalences of categories. 相似文献
96.
本文证明了左n-角范畴的稳定化范畴具有n-角结构,并证明了当n为奇数时,左n-角范畴的Grothendieck群与其稳定化范畴的Grothendieck群同构. 相似文献
97.
98.
Tim Cramer 《Advances in Mathematics》2010,224(3):1097-1120
We show that the reduced Drinfeld double of the Ringel-Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of Burban and Schiffmann [5] and [006], Sevenhant and Van den Bergh (1999) [25], and Xiao and Yang (2001) [31]. 相似文献
99.
Philippe Moser 《Mathematical Logic Quarterly》2010,56(5):461-469
This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp‐computable functions (computable Lebesgue integrable functions) with a size notion, by introducing Lp‐computable Baire categories. We show that Lp‐computable Baire categories satisfy the following three basic properties. Singleton sets {f } (where f is Lp‐computable) are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp‐computable functions is not meager. We give an alternative characterization of meager sets via Banach‐Mazur games. We study the convergence of Fourier series for Lp‐computable functions and show that whereas for every p > 1, the Fourier series of every Lp‐computable function f converges to f in the Lp norm, the set of L1‐computable functions whose Fourier series does not diverge almost everywhere is meager (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
100.
Ned Feng ZHENG 《数学研究与评论》2010,30(2)
In this paper we introduce the notion of (f,ω)-compatible pair (B,H), by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H. 相似文献