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Applied Categorical Structures最新文献

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Derived Projective Covers and Koszul Duality of Simple-Minded and Silting Collections 简单和淤积收藏品的衍生投影盖和Koszul二元性
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-02-01 DOI: 10.1007/s10485-025-09823-1
Lukas Bonfert
{"title":"Derived Projective Covers and Koszul Duality of Simple-Minded and Silting Collections","authors":"Lukas Bonfert","doi":"10.1007/s10485-025-09823-1","DOIUrl":"10.1007/s10485-025-09823-1","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce derived projective covers and explain how they are related to the notion of enough derived projectives. This provides an if-and-only-if criterion for when derived projective covers form a silting collection. We prove moreover a Koszul duality result for silting and simple-minded collections.</p>\u0000 </div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09823-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146096271","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
Projective Crossed Modules in Semi-abelian Categories 半abel范畴中的射影交叉模
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-01-07 DOI: 10.1007/s10485-025-09828-w
Maxime Culot
{"title":"Projective Crossed Modules in Semi-abelian Categories","authors":"Maxime Culot","doi":"10.1007/s10485-025-09828-w","DOIUrl":"10.1007/s10485-025-09828-w","url":null,"abstract":"<div><p>We characterize projective objects in the category of internal crossed modules within any semi-abelian category. When this category forms a variety of algebras, the internal crossed modules again constitute a semi-abelian variety, ensuring the existence of free objects, and thus of enough projectives. We show that such a variety is not necessarily Schreier, but satisfies the so-called Condition (P)—meaning the class of projectives is closed under protosplit subobjects—if and only if the base variety satisfies this condition. As a consequence, the non-additive left chain-derived functors of the connected components functor are well defined in this context.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930244","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
Hopf Categories Associated to Comonoidal Functors 与共形函子相关的Hopf类
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-01-03 DOI: 10.1007/s10485-025-09843-x
Andrea Rivezzi
{"title":"Hopf Categories Associated to Comonoidal Functors","authors":"Andrea Rivezzi","doi":"10.1007/s10485-025-09843-x","DOIUrl":"10.1007/s10485-025-09843-x","url":null,"abstract":"<div><p>We provide an explicit construction of Hopf categories associated to comonoidal functors, generalizing Ševera’s construction of Hopf monoids through <i>M</i>-adapted functors. We discuss the example of the Hopf category whose underlying class is the set of twists of a Lie bialgebra. Finally, we apply the result to the setting of deformed categories.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09843-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929996","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
On Some Triangulated Categories Over Group Algebras 群代数上的一些三角化范畴
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-12-24 DOI: 10.1007/s10485-025-09841-z
Ioannis Emmanouil, Wei Ren
{"title":"On Some Triangulated Categories Over Group Algebras","authors":"Ioannis Emmanouil,&nbsp;Wei Ren","doi":"10.1007/s10485-025-09841-z","DOIUrl":"10.1007/s10485-025-09841-z","url":null,"abstract":"<div><p>In this paper, we introduce the cofibrant derived category of a group algebra <i>kG</i> and study its relation to the derived category of <i>kG</i>. We also define the cofibrant singularity category of <i>kG</i>, whose triviality characterizes the regularity of <i>kG</i> with respect to the cofibrant dimension, and examine its significance as a measure of the obstruction to the equality between the classes of Gorenstein projective and cofibrant modules. We show that the same obstruction can be measured by certain localization sequences between stable categories.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831269","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
Prenormal Categories Prenormal类别
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-12-23 DOI: 10.1007/s10485-025-09835-x
Sandra Mantovani, Mariano Messora
{"title":"Prenormal Categories","authors":"Sandra Mantovani,&nbsp;Mariano Messora","doi":"10.1007/s10485-025-09835-x","DOIUrl":"10.1007/s10485-025-09835-x","url":null,"abstract":"<div><p>In this paper we introduce the notion of (pointed) <i>prenormal category</i>, modelled after regular categories, but with the key notions of coequaliser and kernel pair replaced by those of cokernel and kernel. This framework provides a natural setting for extending certain classical results in algebra. We study the fundamental properties of prenormal categories, including a characterisation in terms of a factorisation system involving normal epimorphisms, and a categorical version of Noether’s so-called ‘third isomorphism theorem’. We also present a range of examples, with the category of commutative monoids constituting a central one. In the second part of the paper we extend prenormality and its related properties to the non-pointed context, using kernels and cokernels defined relative to a distinguished class of trivial objects.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09835-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831328","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
Involutive Quantales and Quantale-Enriched Involutive Topological Spaces 对合量子与富量子对合拓扑空间
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-12-20 DOI: 10.1007/s10485-025-09831-1
Javier Gutiérrez García, Ulrich Höhle
{"title":"Involutive Quantales and Quantale-Enriched Involutive Topological Spaces","authors":"Javier Gutiérrez García,&nbsp;Ulrich Höhle","doi":"10.1007/s10485-025-09831-1","DOIUrl":"10.1007/s10485-025-09831-1","url":null,"abstract":"<div><p>In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic involution, facilitating a balanced topologization of the spectrum of unital <span>(C^*)</span>-algebras that encompasses both closed right and left ideals through the concept of quantic frames. Specifically, certain subspaces of pure states are identified as strongly Hausdorff separated, involutive quantale-enriched topological spaces.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09831-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831146","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
Why is the Category of Near-Vector Spaces Abelian? 为什么近向量空间的范畴是阿贝尔的？
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-12-10 DOI: 10.1007/s10485-025-09837-9
Zurab Janelidze, Sophie Marques, Daniella Moore
{"title":"Why is the Category of Near-Vector Spaces Abelian?","authors":"Zurab Janelidze,&nbsp;Sophie Marques,&nbsp;Daniella Moore","doi":"10.1007/s10485-025-09837-9","DOIUrl":"10.1007/s10485-025-09837-9","url":null,"abstract":"<div><p>In this paper we present a unified proof of the fact that the category of modules over a ring and the category of near-vector spaces in the sense of J. André, over an appropriate scalar system (a ‘scalar group’), are both abelian categories. The unification is possible by viewing each of these categories as subcategories of the (abelian) category of modules over a multiplicative monoid <i>M</i>. Although in the case of near-vector spaces all elements of <i>M</i> except one (the ‘zero’ element) are invertible, we show that this requirement is not necessary for the corresponding category to be abelian in analogy to the well-known fact that modules over a ring form an abelian category even if the ring is not a field (i.e., modules over it are not vector spaces).</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729905","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
Lifting Independence Along Functors 沿函子提升独立性
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-12-07 DOI: 10.1007/s10485-025-09826-y
M. Kamsma, J. Rosický
{"title":"Lifting Independence Along Functors","authors":"M. Kamsma,&nbsp;J. Rosický","doi":"10.1007/s10485-025-09826-y","DOIUrl":"10.1007/s10485-025-09826-y","url":null,"abstract":"<div>\u0000 \u0000 <p>Given a functor <span>(F: mathcal {C}rightarrow mathcal {D})</span> and a model-theoretic independence relation on <span>(mathcal {D})</span>, we can lift that independence relation along <i>F</i> to <span>(mathcal {C})</span> by declaring a commuting square in <span>(mathcal {C})</span> to be independent if its image under <i>F</i> is independent. For each property of interest that an independence relation can have we give assumptions on the functor that guarantee the property to be lifted.</p>\u0000 </div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09826-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729804","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
Scott Locales 当地斯科特
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-12-03 DOI: 10.1007/s10485-025-09839-7
Pedro Resende, João Paulo Santos
{"title":"Scott Locales","authors":"Pedro Resende,&nbsp;João Paulo Santos","doi":"10.1007/s10485-025-09839-7","DOIUrl":"10.1007/s10485-025-09839-7","url":null,"abstract":"<div><p>We prove some facts about locales <i>L</i> equipped with the Scott topology <span>({Omega }(L))</span>, in particular studying a canonical frame homomorphism <span>(phi :{Omega }(L)rightarrow L)</span> which is motivated by an application to cognitive science. Such a topological locale <i>L</i> is called a <i>Scott locale</i> if the inclusion of primes <span>(p:{Sigma }(L)rightarrow L)</span> is continuous. We prove that the spectrum <span>({Sigma }(L))</span> of a Scott locale <i>L</i> is necessarily <span>(T_1)</span>, and that preregular locales (a generalization of regular locales) are Scott locales. If <i>L</i> is the topology of a topological space <i>X</i> we find a (necessarily unique) continuous map <span>(f:Xrightarrow L)</span> such that <span>(f^{-1}=phi )</span> and compare it with the points-to-primes map <span>(p:Xrightarrow L)</span>, showing that <span>(f=p)</span> if and only if <i>X</i> is preregular, and that a sober space <i>X</i> is Hausdorff if and only if <i>X</i> is <span>(T_1)</span> and <span>(f(X)subseteq {Sigma }(L).)</span></p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145659382","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
Associated Sheaf Functors in tt-Geometry 几何中的关联束函子
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2025-11-25 DOI: 10.1007/s10485-025-09824-0
James Rowe
{"title":"Associated Sheaf Functors in tt-Geometry","authors":"James Rowe","doi":"10.1007/s10485-025-09824-0","DOIUrl":"10.1007/s10485-025-09824-0","url":null,"abstract":"<div><p>Given a tensor triangulated category we investigate the geometry of the Balmer spectrum as a locally ringed space by constructing functors assigning to every object in the category a corresponding sheaf of modules over the structure sheaf of the spectrum. Taking the support of these associated sheaves recovers a notion of support based on local categories. We compare this support to the usual support in tt-geometry and show that under reasonable conditions they agree on compact objects. We show that when the tt-category satisfies a scheme-like property, then the sheaves associated to objects are quasi-coherent, and that in the presence of an appropriate t-structure and affine assumption, this sheaf is in fact the sheaf associated to the object’s zeroth cohomology. </p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"33 6","pages":""},"PeriodicalIF":0.5,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09824-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612553","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
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