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Admissibility of Localizations of Crossed Modules 交叉模块局部化的可接受性
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-09-08 DOI: 10.1007/s10485-023-09738-9
Olivia Monjon, Jérôme Scherer, Florence Sterck
{"title":"Admissibility of Localizations of Crossed Modules","authors":"Olivia Monjon,&nbsp;Jérôme Scherer,&nbsp;Florence Sterck","doi":"10.1007/s10485-023-09738-9","DOIUrl":"10.1007/s10485-023-09738-9","url":null,"abstract":"<div><p>The correspondence between the concept of conditional flatness and admissibility in the sense of Galois appears in the context of localization functors in any semi-abelian category admitting a fiberwise localization. It is then natural to wonder what happens in the category of crossed modules where fiberwise localization is not always available. In this article, we establish an equivalence between conditional flatness and admissibility in the sense of Galois (for the class of regular epimorphisms) for regular-epi localization functors. We use this equivalence to prove that nullification functors are admissible for the class of regular epimorphisms, even if the kernels of their localization morphisms are not acyclic.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09738-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50015273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Halmos–von Neumann Theorem for Actions of General Groups 一般群作用的Halmos-von Neumann定理
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-09-08 DOI: 10.1007/s10485-023-09743-y
Patrick Hermle, Henrik Kreidler
{"title":"A Halmos–von Neumann Theorem for Actions of General Groups","authors":"Patrick Hermle,&nbsp;Henrik Kreidler","doi":"10.1007/s10485-023-09743-y","DOIUrl":"10.1007/s10485-023-09743-y","url":null,"abstract":"<div><p>We give a new categorical approach to the Halmos–von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete spectrum are equivalent. This allows to prove the Halmos–von Neumann theorem in the framework of topological dynamics. We then use the Pontryagin and Tannaka–Krein duality theories to obtain classification results for topological and then measure-preserving systems with discrete spectrum. As a byproduct, we obtain a complete isomorphism invariant for compactifications of a fixed topological group.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09743-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41765715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Correction: Presenting Quotient Locales 更正:呈现商区域
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-09-07 DOI: 10.1007/s10485-023-09745-w
Graham Manuell
{"title":"Correction: Presenting Quotient Locales","authors":"Graham Manuell","doi":"10.1007/s10485-023-09745-w","DOIUrl":"10.1007/s10485-023-09745-w","url":null,"abstract":"","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09745-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43379554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coactions on (C^*)-Algebras and Universal Properties (C^*) -代数上的协同作用与全称性质
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-09-07 DOI: 10.1007/s10485-023-09741-0
Erik Bédos, S. Kaliszewski, John Quigg, Jonathan Turk
{"title":"Coactions on (C^*)-Algebras and Universal Properties","authors":"Erik Bédos,&nbsp;S. Kaliszewski,&nbsp;John Quigg,&nbsp;Jonathan Turk","doi":"10.1007/s10485-023-09741-0","DOIUrl":"10.1007/s10485-023-09741-0","url":null,"abstract":"<div><p>It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50013755","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
Deriving Dualities in Pointfree Topology from Priestley Duality 从Priestley对偶导出无点拓扑中的对偶
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-09-01 DOI: 10.1007/s10485-023-09739-8
G. Bezhanishvili, S. Melzer
{"title":"Deriving Dualities in Pointfree Topology from Priestley Duality","authors":"G. Bezhanishvili,&nbsp;S. Melzer","doi":"10.1007/s10485-023-09739-8","DOIUrl":"10.1007/s10485-023-09739-8","url":null,"abstract":"<div><p>There are several prominent duality results in pointfree topology. Hofmann–Lawson duality establishes that the category of continuous frames is dually equivalent to the category of locally compact sober spaces. This restricts to a dual equivalence between the categories of stably continuous frames and stably locally compact spaces, which further restricts to Isbell duality between the categories of compact regular frames and compact Hausdorff spaces. We show how to derive these dualities from Priestley duality for distributive lattices, thus shedding new light on these classic results.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42602443","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
Extension of Topological Groupoids and Hurewicz Morphisms 拓扑群类群与Hurewicz态射的推广
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-08-28 DOI: 10.1007/s10485-023-09744-x
Saikat Chatterjee, Praphulla Koushik
{"title":"Extension of Topological Groupoids and Hurewicz Morphisms","authors":"Saikat Chatterjee,&nbsp;Praphulla Koushik","doi":"10.1007/s10485-023-09744-x","DOIUrl":"10.1007/s10485-023-09744-x","url":null,"abstract":"<div><p>In this paper, we introduce the notion of a topological groupoid extension and relate it to the already existing notion of a gerbe over a topological stack. We further study the properties of a gerbe over a Hurewicz (resp. Serre) stack.\u0000\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09744-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44009957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hopf Monads: A Survey with New Examples and Applications Hopf单子:新例子和应用综述
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-08-27 DOI: 10.1007/s10485-023-09732-1
Aryan Ghobadi
{"title":"Hopf Monads: A Survey with New Examples and Applications","authors":"Aryan Ghobadi","doi":"10.1007/s10485-023-09732-1","DOIUrl":"10.1007/s10485-023-09732-1","url":null,"abstract":"<div><p>We survey the theory of Hopf monads on monoidal categories, and present new examples and applications. As applications, we utilise this machinery to present a new theory of cross products, as well as analogues of the Fundamental Theorem of Hopf algebras and Radford’s biproduct Theorem for Hopf algebroids. Additionally, we describe new examples of Hopf monads which arise from Galois and Ore extensions of bialgebras. We also classify Lawvere theories whose corresponding monads on the category of sets and functions become Hopf, as well as Hopf monads on the poset of natural numbers.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09732-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41933969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions 逆半群正交作用的极大序Groupoid和Galois对应
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-08-21 DOI: 10.1007/s10485-023-09742-z
Wesley G. Lautenschlaeger, Thaísa Tamusiunas
{"title":"Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions","authors":"Wesley G. Lautenschlaeger,&nbsp;Thaísa Tamusiunas","doi":"10.1007/s10485-023-09742-z","DOIUrl":"10.1007/s10485-023-09742-z","url":null,"abstract":"<div><p>We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, to prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44517564","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
Categorical View of the Partite Lemma in Structural Ramsey Theory 结构拉姆齐理论中部引理的范畴观
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-08-04 DOI: 10.1007/s10485-023-09733-0
Sebastian Junge
{"title":"Categorical View of the Partite Lemma in Structural Ramsey Theory","authors":"Sebastian Junge","doi":"10.1007/s10485-023-09733-0","DOIUrl":"10.1007/s10485-023-09733-0","url":null,"abstract":"<div><p>We construct the main object of the Partite Lemma as the colimit over a certain diagram. This gives a purely category theoretic take on the Partite Lemma and establishes the canonicity of the object. Additionally, the categorical point of view allows us to unify the direct Partite Lemma in Nešetřil and Rödl (J Comb Theory Ser A 22(3):289–312, 1977; J Comb Theory Ser A 34(2):183–201, 1983; Discrete Math 75(1–3):327–334, 1989) with the dual Paritite Lemma in Solecki (J Comb Theory Ser A 117(6):704–714, 2010).</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09733-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48305338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Weighted Colimits of 2-Representations and Star Algebras 2-表示与星形代数的加权极限
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-07-22 DOI: 10.1007/s10485-023-09737-w
Mateusz Stroiński
{"title":"Weighted Colimits of 2-Representations and Star Algebras","authors":"Mateusz Stroiński","doi":"10.1007/s10485-023-09737-w","DOIUrl":"10.1007/s10485-023-09737-w","url":null,"abstract":"<div><p>We apply the theory of weighted bicategorical colimits to study the problem of existence and computation of such colimits of birepresentations of finitary bicategories. The main application of our results is the complete classification of simple transitive birepresentations of a bicategory studied previously by Zimmermann. The classification confirms a conjecture he has made.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09737-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47559798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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