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Applied Categorical Structures最新文献

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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
Presenting Quotient Locales 表示商区域
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-07-21 DOI: 10.1007/s10485-023-09736-x
Graham Manuell
{"title":"Presenting Quotient Locales","authors":"Graham Manuell","doi":"10.1007/s10485-023-09736-x","DOIUrl":"10.1007/s10485-023-09736-x","url":null,"abstract":"<div><p>It is often useful to be able to deal with locales in terms of presentations of their underlying frames, or equivalently, the geometric theories which they classify. Given a presentation for a locale, presentations for its sublocales can be obtained by simply appending additional relations, but the case of quotient locales is more subtle. We provide simple procedures for obtaining presentations of open quotients, proper quotients or general triquotients from presentations of the parent locale. The results are proved with the help of the suplattice, preframe and dcpo coverage theorems and applied to obtain presentations of the circle from ones for <span>(mathbb {R})</span> and [0, 1].</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09736-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42361339","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
Yoneda Lemma for Simplicial Spaces 简单空间的Yoneda引理
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-07-11 DOI: 10.1007/s10485-023-09734-z
Nima Rasekh
{"title":"Yoneda Lemma for Simplicial Spaces","authors":"Nima Rasekh","doi":"10.1007/s10485-023-09734-z","DOIUrl":"10.1007/s10485-023-09734-z","url":null,"abstract":"<div><p>We study the Yoneda lemma for arbitrary simplicial spaces. We do that by introducing <i>left fibrations</i> of simplicial spaces and studying their associated model structure, the <i>covariant model structure</i>. In particular, we prove a <i>recognition principle</i> for covariant equivalences over an arbitrary simplicial space and <i>invariance</i> of the covariant model structure with respect to complete Segal space equivalences.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09734-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42970719","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: 19
R-Linear Triangulated Categories and Stability Conditions R-线性三角范畴及其稳定性条件
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-06-29 DOI: 10.1007/s10485-023-09731-2
Kotaro Kawatani, Hiroyuki Minamoto
{"title":"R-Linear Triangulated Categories and Stability Conditions","authors":"Kotaro Kawatani,&nbsp;Hiroyuki Minamoto","doi":"10.1007/s10485-023-09731-2","DOIUrl":"10.1007/s10485-023-09731-2","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative ring. We introduce the notion of support of a object in an <i>R</i>-linear triangulated category. As an application, we study the non-existence of Bridgeland stability condition on <i>R</i>-linear triangulated categories.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42613343","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
Correction to: Ramsey Properties of Products and Pullbacks of Categories and the Grothendieck Construction 修正：乘积的Ramsey性质和范畴的回调与Grothendieck构造
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-06-12 DOI: 10.1007/s10485-023-09730-3
Dragan Mašulović
{"title":"Correction to: Ramsey Properties of Products and Pullbacks of Categories and the Grothendieck Construction","authors":"Dragan Mašulović","doi":"10.1007/s10485-023-09730-3","DOIUrl":"10.1007/s10485-023-09730-3","url":null,"abstract":"","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48353194","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
De Vries Powers and Proximity Specker Algebras De Vries幂与邻近Specker代数
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-04-21 DOI: 10.1007/s10485-023-09714-3
G. Bezhanishvili, L. Carai, P. J. Morandi, B. Olberding
{"title":"De Vries Powers and Proximity Specker Algebras","authors":"G. Bezhanishvili,&nbsp;L. Carai,&nbsp;P. J. Morandi,&nbsp;B. Olberding","doi":"10.1007/s10485-023-09714-3","DOIUrl":"10.1007/s10485-023-09714-3","url":null,"abstract":"<div><p>By de Vries duality, the category <span>(textsf {KHaus})</span> of compact Hausdorff spaces is dually equivalent to the category <span>(textsf {DeV})</span> of de Vries algebras. There is a similar duality for <span>(textsf {KHaus})</span>, where de Vries algebras are replaced by proximity Baer-Specker algebras. The functor associating with each compact Hausdorff space a proximity Baer-Specker algebra is described by generalizing the notion of a boolean power of a totally ordered domain to that of a de Vries power. It follows that <span>(textsf {DeV})</span> is equivalent to the category <span>(text {textsf{PBSp}})</span> of proximity Baer-Specker algebras. The equivalence is obtained by passing through <span>(textsf {KHaus})</span>, and hence is not choice-free. In this paper we give a direct algebraic proof of this equivalence, which is choice-independent. To do so, we give an alternate choice-free description of de Vries powers of a totally ordered domain.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09714-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48156056","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
Additive Grothendieck Pretopologies and Presentations of Tensor Categories 张量范畴的加性Grothendieck预拓扑与表示
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-04-20 DOI: 10.1007/s10485-023-09722-3
Kevin Coulembier
{"title":"Additive Grothendieck Pretopologies and Presentations of Tensor Categories","authors":"Kevin Coulembier","doi":"10.1007/s10485-023-09722-3","DOIUrl":"10.1007/s10485-023-09722-3","url":null,"abstract":"<div><p>We study how tensor categories can be presented in terms of rigid monoidal categories and Grothendieck topologies and show that such presentations lead to strong universal properties. As the main tool in this study, we define a notion on preadditive categories which plays a role similar to (a generalisation of) the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology defines an additive Grothendieck topology and suffices to define the sheaf category. This new notion also allows us to study the noetherian and subcanonical nature of additive topologies, to describe easily the join of a family of additive topologies and to identify useful universal properties of the sheaf category.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09722-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46010150","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: 5
Profunctors Between Posets and Alexander Duality 偏序集与亚历山大对偶之间的Profunctors
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-04-10 DOI: 10.1007/s10485-023-09711-6
Gunnar Fløystad
{"title":"Profunctors Between Posets and Alexander Duality","authors":"Gunnar Fløystad","doi":"10.1007/s10485-023-09711-6","DOIUrl":"10.1007/s10485-023-09711-6","url":null,"abstract":"<div><p>We consider profunctors <img> between posets and introduce their <i>graph</i> and <i>ascent</i>. The profunctors <span>(text {Pro}(P,Q))</span> form themselves a poset, and we consider a partition <span>(mathcal {I}sqcup mathcal {F})</span> of this into a down-set <span>(mathcal {I})</span> and up-set <span>(mathcal {F})</span>, called a <i>cut</i>. To elements of <span>(mathcal {F})</span> we associate their graphs, and to elements of <span>(mathcal {I})</span> we associate their ascents. Our basic results is that this, suitably refined, preserves being a cut: We get a cut in the Boolean lattice of subsets of the underlying set of <span>(Q times P)</span>. Cuts in finite Booleans lattices correspond precisely to finite simplicial complexes. We apply this in commutative algebra where these give classes of Alexander dual square-free monomial ideals giving the full and natural generalized setting of isotonian ideals and letterplace ideals for posets. We study <span>(text {Pro}({mathbb N}, {mathbb N}))</span>. Such profunctors identify as order preserving maps <span>(f: {mathbb N}rightarrow {mathbb N}cup {infty })</span>. For our applications when <i>P</i> and <i>Q</i> are infinite, we also introduce a topology on <span>(text {Pro}(P,Q))</span>, in particular on profunctors <span>(text {Pro}({mathbb N},{mathbb N}))</span>.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09711-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45555584","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: 3
Inner Automorphisms of Presheaves of Groups 群的Presheaves的内自同构
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-04-08 DOI: 10.1007/s10485-023-09720-5
Jason Parker
{"title":"Inner Automorphisms of Presheaves of Groups","authors":"Jason Parker","doi":"10.1007/s10485-023-09720-5","DOIUrl":"10.1007/s10485-023-09720-5","url":null,"abstract":"<div><p>It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely <i>categorically</i> as those group automorphisms that can be coherently extended along any outgoing homomorphism. One is thus motivated to define a notion of <i>(categorical) inner automorphism</i> in an arbitrary category, as an automorphism that can be coherently extended along any outgoing morphism, and the theory of such automorphisms forms part of the theory of <i>covariant isotropy</i>. In this paper, we prove that the categorical inner automorphisms in any category <span>(textsf{Group}^mathcal {J})</span> of presheaves of groups can be characterized in terms of conjugation-theoretic inner automorphisms of the component groups, together with a natural automorphism of the identity functor on the index category <span>(mathcal {J})</span>. In fact, we deduce such a characterization from a much more general result characterizing the categorical inner automorphisms in any category <span>(mathbb {T}textsf{mod}^mathcal {J})</span> of presheaves of <span>(mathbb {T})</span>-models for a suitable first-order theory <span>(mathbb {T})</span>.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09720-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41787078","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: 3
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