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Bulletin of the Belgian Mathematical Society-Simon Stevin最新文献

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Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations 裂裂纤颤的柯西完备性、松弛表胚及有效下降
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-10-21 DOI: 10.36045/j.bbms.221021
Fernando Lucatelli Nunes, Rui Prezado, L. Sousa
{"title":"Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations","authors":"Fernando Lucatelli Nunes, Rui Prezado, L. Sousa","doi":"10.36045/j.bbms.221021","DOIUrl":"https://doi.org/10.36045/j.bbms.221021","url":null,"abstract":"For any suitable base category $mathcal{V} $, we find that $mathcal{V} $-fully faithful lax epimorphisms in $mathcal{V} $-$mathsf{Cat} $ are precisely those $mathcal{V}$-functors $F colon mathcal{A} to mathcal{B}$ whose induced $mathcal{V} $-functors $mathsf{Cauchy} F colon mathsf{Cauchy} mathcal{A} to mathsf{Cauchy} mathcal{B} $ between the Cauchy completions are equivalences. For the case $mathcal{V} = mathsf{Set} $, this is equivalent to requiring that the induced functor $mathsf{CAT} left( F,mathsf{Cat}right) $ between the categories of split (op)fibrations is an equivalence. By reducing the study of effective descent functors with respect to the indexed category of split (op)fibrations $mathcal{F}$ to the study of the codescent factorization, we find that these observations on fully faithful lax epimorphisms provide us with a characterization of (effective) $mathcal{F}$-descent morphisms in the category of small categories $mathcal{Cat}$; namely, we find that they are precisely the (effective) descent morphisms with respect to the indexed categories of discrete opfibrations -- previously studied by Sobral. We include some comments on the Beck-Chevalley condition and future work.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76412035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classification of finite-dimensional Hopf algebras over dual Radford algebras 对偶Radford代数上有限维Hopf代数的分类
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-09-15 DOI: 10.36045/j.bbms.210612
Rongchuan Xiong, N. Hu
{"title":"Classification of finite-dimensional Hopf algebras over dual Radford algebras","authors":"Rongchuan Xiong, N. Hu","doi":"10.36045/j.bbms.210612","DOIUrl":"https://doi.org/10.36045/j.bbms.210612","url":null,"abstract":". We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension 4 p for a prime p > 5. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73951727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Cofiniteness of generalized local cohomology modules with respect to the class of modules in dimension less than a fixed integer 广义局部上同模对维数小于固定整数的模类的共性
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-09-15 DOI: 10.36045/j.bbms.201230
A. Vahidi, Saeid Morsali
{"title":"Cofiniteness of generalized local cohomology modules with respect to the class of modules in dimension less than a fixed integer","authors":"A. Vahidi, Saeid Morsali","doi":"10.36045/j.bbms.201230","DOIUrl":"https://doi.org/10.36045/j.bbms.201230","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79388267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A new approach to the three bisectors problem 三等分线问题的一种新方法
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-09-15 DOI: 10.36045/j.bbms.211105
D. Marinescu, Eugen Păltănea
{"title":"A new approach to the three bisectors problem","authors":"D. Marinescu, Eugen Păltănea","doi":"10.36045/j.bbms.211105","DOIUrl":"https://doi.org/10.36045/j.bbms.211105","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80019727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mapping properties of the fractional integral operators on Herz-Hardy spaces with variable exponents 变指数Herz-Hardy空间上分数阶积分算子的映射性质
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-09-15 DOI: 10.36045/j.bbms.211026
K. Ho
{"title":"Mapping properties of the fractional integral operators on Herz-Hardy spaces with variable exponents","authors":"K. Ho","doi":"10.36045/j.bbms.211026","DOIUrl":"https://doi.org/10.36045/j.bbms.211026","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88136233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Distinguished vector-valued continuous function spaces and injective tensor products 区分向量值连续函数空间与内射张量积
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-09-15 DOI: 10.36045/j.bbms.210812
J. C. Ferrando, J. Ka̧kol
{"title":"Distinguished vector-valued continuous function spaces and injective tensor products","authors":"J. C. Ferrando, J. Ka̧kol","doi":"10.36045/j.bbms.210812","DOIUrl":"https://doi.org/10.36045/j.bbms.210812","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85592261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Jet schemes of quasi-homogeneous hypersurfaces and motivic monodromy conjecture for isolated quasi-homogeneous hypersurface singularities 拟齐次超曲面的射流格式及孤立拟齐次超曲面奇点的动力单性猜想
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-09-15 DOI: 10.36045/j.bbms.210506
J. Sebag
{"title":"Jet schemes of quasi-homogeneous hypersurfaces and motivic monodromy conjecture for isolated quasi-homogeneous hypersurface singularities","authors":"J. Sebag","doi":"10.36045/j.bbms.210506","DOIUrl":"https://doi.org/10.36045/j.bbms.210506","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89241230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Uniformities and a quantale structure on localic groups 局部群上的均匀性和量子结构
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-05-01 DOI: 10.36045/j.bbms.210823
J. Picado, A. Pultr
{"title":"Uniformities and a quantale structure on localic groups","authors":"J. Picado, A. Pultr","doi":"10.36045/j.bbms.210823","DOIUrl":"https://doi.org/10.36045/j.bbms.210823","url":null,"abstract":"of their size), the idea of shifting neighbourhoods of the group unit via the translation homeomorphisms do not work. Despite this difficulty, the paper proves that there are again induced uniformities (both of Tukey or Weil type) and the two are equivalent. The major tool in the paper is that of a special type of involutive quantale (called G -quantale ), which is borne out of the group structure of the locale. Such quantales are investigated and characterised paving the path to formulating proper-ties of the enriched quantales from which the group structure can be reconstructed. The localic group homomorphisms then turn out to be in one to one correspondence with quantale homomorphisms. Finally, the G -quantales are also ordered semigroups and hence can be used as a set of values for a generalised metric. The paper shows the natural group uniformities are metric uniformities of thus generalised metrics.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83347148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Colorful Carathéodory, Helly and Sierksma numbers of convexity spaces 彩色的carath<s:1>奥多里、Helly和Sierksma凸空间数
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-05-01 DOI: 10.36045/j.bbms.210414
Krzysztof Kołodziejczyk
{"title":"Colorful Carathéodory, Helly and Sierksma numbers of convexity spaces","authors":"Krzysztof Kołodziejczyk","doi":"10.36045/j.bbms.210414","DOIUrl":"https://doi.org/10.36045/j.bbms.210414","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81818165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Completeness in topological vector spaces and filters on $mathbb N$ 拓扑向量空间的完备性和$mathbb N$上的滤波器
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-05-01 DOI: 10.36045/j.bbms.210512
V. Kadets, D. Seliutin
{"title":"Completeness in topological vector spaces and filters on $mathbb N$","authors":"V. Kadets, D. Seliutin","doi":"10.36045/j.bbms.210512","DOIUrl":"https://doi.org/10.36045/j.bbms.210512","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84105744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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