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Applied Categorical Structures最新文献

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Minimal Models of Some Differential Graded Modules 一类微分梯度模的极小模型
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-01-03 DOI: 10.1007/s10485-022-09708-7
Berrin Şentürk, Özgün Ünlü
{"title":"Minimal Models of Some Differential Graded Modules","authors":"Berrin Şentürk,&nbsp;Özgün Ünlü","doi":"10.1007/s10485-022-09708-7","DOIUrl":"10.1007/s10485-022-09708-7","url":null,"abstract":"<div><p>Minimal models of chain complexes associated with free torus actions on spaces have been extensively studied in the literature. In this paper, we discuss these constructions using the language of operads. The main goal of this paper is to define a new Koszul operad that has projections onto several of the operads used in these minimal model constructions.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50006606","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
Operators Between Classes of Modules Given by Preradicals 由泛型给出的模块类之间的操作符
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-01-01 DOI: 10.1007/s10485-022-09702-z
Alejandro Alvarado García, César Cejudo Castilla, Mauricio Medina Bárcenas, Ivan Fernando Vilchis Montalvo
{"title":"Operators Between Classes of Modules Given by Preradicals","authors":"Alejandro Alvarado García,&nbsp;César Cejudo Castilla,&nbsp;Mauricio Medina Bárcenas,&nbsp;Ivan Fernando Vilchis Montalvo","doi":"10.1007/s10485-022-09702-z","DOIUrl":"10.1007/s10485-022-09702-z","url":null,"abstract":"","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":"1"},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09702-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50037081","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
Ramsey Properties of Products and Pullbacks of Categories and the Grothendieck Construction 产品的Ramsey性质、类别的回调与Grothendieck构造
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-12-29 DOI: 10.1007/s10485-022-09700-1
Dragan Mašulović
{"title":"Ramsey Properties of Products and Pullbacks of Categories and the Grothendieck Construction","authors":"Dragan Mašulović","doi":"10.1007/s10485-022-09700-1","DOIUrl":"10.1007/s10485-022-09700-1","url":null,"abstract":"<div><p>In this paper we provide purely categorical proofs of two important results of structural Ramsey theory: the result of M. Sokić that the free product of Ramsey classes is a Ramsey class, and the result of M. Bodirsky, M. Pinsker and T. Tsankov that adding constants to the language of a Ramsey class preserves the Ramsey property. The proofs that we present here ignore the model-theoretic background of these statements. Instead, they focus on categorical constructions by which the classes can be constructed generalizing the original statements along the way. It turns out that the restriction to classes of relational structures, although fundamental for the original proof strategies, is not relevant for the statements themselves. The categorical proofs we present here remove all restrictions on the signature of first-order structures and provide the information not only about the Ramsey property but also about the Ramsey degrees.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45814455","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
Unitless Frobenius Quantales Unitless Frobenius Quantales
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-12-27 DOI: 10.1007/s10485-022-09699-5
Cédric de Lacroix, Luigi Santocanale
{"title":"Unitless Frobenius Quantales","authors":"Cédric de Lacroix,&nbsp;Luigi Santocanale","doi":"10.1007/s10485-022-09699-5","DOIUrl":"10.1007/s10485-022-09699-5","url":null,"abstract":"<div><p>It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define Frobenius quantales that may not have a unit. We develop the elementary theory of these structures and show, in particular, how to define nuclei whose quotients are Frobenius quantales. This yields a phase semantics and a representation theorem via phase quantales. Important examples of these structures arise from Raney’s notion of tight Galois connection: tight endomaps of a complete lattice always form a Girard quantale which is unital if and only if the lattice is completely distributive. We give a characterisation and an enumeration of tight endomaps of the diamond lattices <span>(M_n)</span> and exemplify the Frobenius structure on these maps. By means of phase semantics, we exhibit analogous examples built up from trace class operators on an infinite dimensional Hilbert space. Finally, we argue that units cannot be properly added to Frobenius quantales: every possible extention to a unital quantale fails to preserve negations.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09699-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45317354","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 Simplicial Category for Higher Correspondences 高等对应的一个简单范畴
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-12-27 DOI: 10.1007/s10485-022-09705-w
Redi Haderi
{"title":"A Simplicial Category for Higher Correspondences","authors":"Redi Haderi","doi":"10.1007/s10485-022-09705-w","DOIUrl":"10.1007/s10485-022-09705-w","url":null,"abstract":"<div><p>In this work we propose a realization of Lurie’s prediction that inner fibrations <span>(p: X rightarrow A)</span> are classified by <i>A</i>-indexed diagrams in a “higher category” whose objects are <span>(infty )</span>-categories, morphisms are correspondences between them and higher morphisms are higher correspondences. We will obtain this as a corollary of a more general result which classifies all simplicial maps between ordinary simplicial sets in a similar fashion. Correspondences between simplicial sets (and <span>(infty )</span>-categories) are a generalization of the concept of profunctor (or bimodule) pertaining to categories. While categories, functors and profunctors are organized in a double category, we will exhibit simplicial sets, simplicial maps, and correspondences as part of a simplicial category. This allows us to make precise statements and provide proofs. Our main tool is the language of double categories, which we use in the context of simplicial categories as well.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43134041","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 Pullback Diagram in the Coarse Category 粗类的回调图
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-12-27 DOI: 10.1007/s10485-022-09707-8
Elisa Hartmann
{"title":"A Pullback Diagram in the Coarse Category","authors":"Elisa Hartmann","doi":"10.1007/s10485-022-09707-8","DOIUrl":"10.1007/s10485-022-09707-8","url":null,"abstract":"<div><p>This paper studies the asymptotic product of two metric spaces. It is well defined if one of the spaces is visual or if both spaces are geodesic. In this case the asymptotic product is the pullback of a limit diagram in the coarse category. Using this product construction we can define a homotopy theory on coarse metric spaces in a natural way. We prove that all finite colimits exist in the coarse category.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47806464","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: 3
q-Tensor and Exterior Centers, Related Degrees and Capability q-张量与外心、相关度和能力
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-12-26 DOI: 10.1007/s10485-022-09701-0
Raimundo Bastos, Ricardo de Oliveira, Guram Donadze, Noraí Romeu Rocco
{"title":"q-Tensor and Exterior Centers, Related Degrees and Capability","authors":"Raimundo Bastos,&nbsp;Ricardo de Oliveira,&nbsp;Guram Donadze,&nbsp;Noraí Romeu Rocco","doi":"10.1007/s10485-022-09701-0","DOIUrl":"10.1007/s10485-022-09701-0","url":null,"abstract":"<div><p>We introduce intermediate commutators and study their degrees. We define <span>((q, {}))</span>-capable groups and prove that a group <i>G</i> is <span>((q, {}))</span>-capable if and only if <span>(Z^{wedge }_{(q, {})}(G)=1)</span>.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09701-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47400970","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
Coactions on C∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C^*$$end{document}-Algebras and Universal Properties 关于C*documentclass[12pt]｛minimum｝usepackage｛amsmath｝usapackage｛wasysym｝use package｛amsfonts｝usepackage｛amssymb｝userpackage｛amsbsy｝ usepackage{mathrsfs｝ userpackage{upgeek｝setlength｛doddsidemargin｝｛-69pt｝ begin｛document｝$C^*$end{document}-Algebras和通用属性
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-12-08 DOI: 10.1007/s10485-023-09741-0
Erik B'edos, S. Kaliszewski, John Quigg, Jonathan Turk
{"title":"Coactions on C∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C^*$$end{document}-Algebras and Universal Properties","authors":"Erik B'edos, S. Kaliszewski, John Quigg, Jonathan Turk","doi":"10.1007/s10485-023-09741-0","DOIUrl":"https://doi.org/10.1007/s10485-023-09741-0","url":null,"abstract":"","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43457547","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
Semantic Factorization and Descent 语义分解与下降
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-11-15 DOI: 10.1007/s10485-022-09694-w
Fernando Lucatelli Nunes
{"title":"Semantic Factorization and Descent","authors":"Fernando Lucatelli Nunes","doi":"10.1007/s10485-022-09694-w","DOIUrl":"10.1007/s10485-022-09694-w","url":null,"abstract":"<div><p>Let <span>({mathbb {A}})</span> be a 2-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism <i>p</i> exists and is preserved by a suitable morphism, the factorization given by the lax descent object of the <i>two-dimensional cokernel diagram</i> of <i>p</i> is up to isomorphism the same as the semantic factorization of <i>p</i>, either one existing if the other does. The result can be seen as a counterpart account to the celebrated Bénabou–Roubaud theorem. This leads in particular to a monadicity theorem, since it characterizes monadicity via descent. It should be noted that all the conditions on the codensity monad of <i>p</i> trivially hold whenever <i>p</i> has a left adjoint and, hence, in this case, we find monadicity to be a two-dimensional exact condition on <i>p</i>, namely, to be an effective faithful morphism of the 2-category <span>({mathbb {A}})</span>.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"30 6","pages":"1393 - 1433"},"PeriodicalIF":0.6,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09694-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45437569","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: 4
2-Cartesian Fibrations I: A Model for (infty )-Bicategories Fibred in (infty )-Bicategories 2-笛卡儿纤颤I:一个模型 (infty )-分类纤维 (infty )-分类
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2022-09-28 DOI: 10.1007/s10485-022-09693-x
Fernando Abellán García, Walker H. Stern
{"title":"2-Cartesian Fibrations I: A Model for (infty )-Bicategories Fibred in (infty )-Bicategories","authors":"Fernando Abellán García,&nbsp;Walker H. Stern","doi":"10.1007/s10485-022-09693-x","DOIUrl":"10.1007/s10485-022-09693-x","url":null,"abstract":"<div><p>In this paper, we provide a notion of <span>(infty )</span>-bicategories fibred in <span>(infty )</span>-bicategories which we call <i>2-Cartesian fibrations</i>. Our definition is formulated using the language of marked biscaled simplicial sets: Those are scaled simplicial sets equipped with an additional collection of triangles containing the scaled 2-simplices, which we call <i>lean triangles</i>, in addition to a collection of edges containing all degenerate 1-simplices. We prove the existence of a left proper combinatorial simplicial model category whose fibrant objects are precisely the 2-Cartesian fibrations over a chosen scaled simplicial set <i>S</i>. Over the terminal scaled simplicial set, this provides a new model structure modeling <span>(infty )</span>-bicategories, which we show is Quillen equivalent to Lurie’s scaled simplicial set model. We conclude by providing a characterization of 2-Cartesian fibrations over an <span>(infty )</span>-bicategory. This characterization then allows us to identify those 2-Cartesian fibrations arising as the coherent nerve of a fibration of <span>({text {Set}}^+_{Delta })</span>-enriched categories, thus showing that our definition recovers the preexisting notions of fibred 2-categories.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"30 6","pages":"1341 - 1392"},"PeriodicalIF":0.6,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50052459","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: 4
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