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Applied Categorical Structures最新文献

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Approximable Triangulated Categories and Reflexive DG-categories 近似三角化范畴与自反dg范畴
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-03-22 DOI: 10.1007/s10485-026-09856-0
Isambard Goodbody
{"title":"Approximable Triangulated Categories and Reflexive DG-categories","authors":"Isambard Goodbody","doi":"10.1007/s10485-026-09856-0","DOIUrl":"10.1007/s10485-026-09856-0","url":null,"abstract":"<div><p>We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable triangulated category under a properness assumption. We apply our results to proper schemes, proper connective DG-algebras and Azumaya algebras over proper schemes. We include an appendix by Raedschelders and Stevenson showing that proper connective DG-algebras admit finite dimensional models over any field.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-026-09856-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560904","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
A Categorical Approach to Additive Combinatorics 加性组合的范畴方法
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-03-22 DOI: 10.1007/s10485-026-09852-4
Saúl A. Blanco, Esfandiar Haghverdi
{"title":"A Categorical Approach to Additive Combinatorics","authors":"Saúl A. Blanco,&nbsp;Esfandiar Haghverdi","doi":"10.1007/s10485-026-09852-4","DOIUrl":"10.1007/s10485-026-09852-4","url":null,"abstract":"<div><p>Motivated by the definition of Freiman homomorphism, we explore the possibilities of formulating some basic notions and techniques of additive combinatorics in a categorical language. We show that additive sets and Freiman homomorphisms form a category and we study several limit and colimit constructions in this category and in one of its interesting subcategories. Moreover, we study the additive structure of these (co)limit objects using the additive doubling constant. We relate this category to that of finite sets and mappings, and to that of abelian groups and group homomorphisms. We show that the Konyagin and Lev result on the existence of universal ambient groups is an instance of an adjunction.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-026-09852-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560905","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
What is Connectivity? 什么是连通性？
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-03-22 DOI: 10.1007/s10485-025-09840-0
Jean F. Du Plessis, Zurab Janelidze, Bernardus A. Wessels
{"title":"What is Connectivity?","authors":"Jean F. Du Plessis,&nbsp;Zurab Janelidze,&nbsp;Bernardus A. Wessels","doi":"10.1007/s10485-025-09840-0","DOIUrl":"10.1007/s10485-025-09840-0","url":null,"abstract":"<div><p>In this paper, we explore a taxonomy of connectivity for space-like structures. It is inspired by isolating posets of connected pieces of a space and examining its embedding in the ambient space. The taxonomy includes in its scope all standard notions of connectivity in point-set and point-free contexts, such as connectivity in graphs and hypergraphs (as well as <i>k</i>-connectivity in graphs), connectivity and path-connectivity in topology, and connectivity of elements in a frame.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560903","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
Closed Subcategories of Quotient Categories 商类的闭子类
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-03-08 DOI: 10.1007/s10485-026-09851-5
Daniel Rogalski
{"title":"Closed Subcategories of Quotient Categories","authors":"Daniel Rogalski","doi":"10.1007/s10485-026-09851-5","DOIUrl":"10.1007/s10485-026-09851-5","url":null,"abstract":"<div><p>We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category <i>X</i>. The closed subcategories are the direct analogs of closed subschemes in the commutative case, in the sense that when <i>X</i> is the category of quasi-coherent sheaves on a quasi-projective scheme <i>S</i>, then the closed subschemes of <i>S</i> correspond bijectively to the closed subcategories of <i>X</i>. Many interesting quasi-schemes, such as the noncommutative projective scheme <span>(operatorname {Qgr-}hspace{-2.0pt}B = operatorname {Gr-}hspace{-2.0pt}B/operatorname {Tors-}hspace{-2.0pt}B)</span> associated to a graded algebra <i>B</i>, arise as quotient categories of simpler abelian categories. In this paper, we will show how to describe the closed subcategories of any quotient category <i>X</i>/<i>Y</i> in terms of closed subcategories of <i>X</i> with special properties, when <i>X</i> is a category with a set of compact projective generators.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-026-09851-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440847","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 Vector Spaces with Formal Infinite Sums 关于形式无穷和的向量空间
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-03-04 DOI: 10.1007/s10485-025-09844-w
Pietro Freni
{"title":"On Vector Spaces with Formal Infinite Sums","authors":"Pietro Freni","doi":"10.1007/s10485-025-09844-w","DOIUrl":"10.1007/s10485-025-09844-w","url":null,"abstract":"<div><p>I discuss possible definitions of categories of vector spaces enriched with a notion of formal infinite linear combination in the likes of the formal infinite linear combinations one has in the context of generalized power series, I call these <i>reasonable categories of strong vector spaces</i> (r.c.s.v.s.). I show that, in a precise sense, the more general possible definition for a strong vector space is that of a small <span>(textrm{Vect})</span>-enriched endofunctor of <span>(textrm{Vect})</span> that is right orthogonal for every cardinal <span>(lambda )</span>, to the cokernel of the canonical inclusion of the <span>(lambda )</span>-th copower in the <span>(lambda )</span>-th power of the identity functor: these form the objects for a universal r.c.s.v.s. I call <span>(Sigma textrm{Vect})</span>. I show this is equivalent to the category of <i>ultrafinite summability spaces</i> defined independently in Bagayoko et al. (Automorphisms and derivations on algebras endowed with formal infinite sums, 2024). I relate this category to what could be understood to be the obvious category of strong vector spaces <span>(BSigma textrm{Vect})</span> and to the r.c.s.v.s. <span>(Ktextrm{TVect}_s)</span> of separated linearly topologized spaces that are generated by linearly compact spaces. I analyze the monoidal closed structures on various r.c.s.v.s. induced by the natural one on <span>(textrm{Ind}{text {-}}(textrm{Vect}^textrm{op}))</span>. In particular with respect to the problem of closure under the tensor product of <span>(textrm{Ind}{text {-}}(textrm{Vect}^textrm{op}))</span>. Most of the technical results apply to a more general class of orthogonal subcategories of <span>(textrm{Ind}{text {-}}(textrm{Vect}^textrm{op}))</span> and I work with that generality as it’s cost-free.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09844-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363207","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
McKinsey-Tarski Algebras and Raney Extensions McKinsey-Tarski代数与Raney扩展
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-03-04 DOI: 10.1007/s10485-026-09849-z
G. Bezhanishvili, R. Raviprakash, A. L. Suarez, J. Walters-Wayland
{"title":"McKinsey-Tarski Algebras and Raney Extensions","authors":"G. Bezhanishvili,&nbsp;R. Raviprakash,&nbsp;A. L. Suarez,&nbsp;J. Walters-Wayland","doi":"10.1007/s10485-026-09849-z","DOIUrl":"10.1007/s10485-026-09849-z","url":null,"abstract":"<div><p>We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing the construction of the Funayama envelope of a frame. The resulting notion of the <span>(T_0)</span>-hull of a Raney extension generalizes that of the <span>(T_D)</span>-hull of a frame.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-026-09849-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363206","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
Roos Axiom Holds for Quasi-Coherent Sheaves 拟相干束的Roos公理成立
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-02-18 DOI: 10.1007/s10485-025-09845-9
Leonid Positselski
{"title":"Roos Axiom Holds for Quasi-Coherent Sheaves","authors":"Leonid Positselski","doi":"10.1007/s10485-025-09845-9","DOIUrl":"10.1007/s10485-025-09845-9","url":null,"abstract":"<div><p>Let <i>X</i> be either a quasi-compact semi-separated scheme, or a Noetherian scheme of finite Krull dimension. We show that the Grothendieck abelian category <span>(X{{mathsf {-Qcoh}}})</span> of quasi-coherent sheaves on <i>X</i> satisfies the Roos axiom <span>(textrm{AB}4^*)</span>-<i>n</i>: the derived functors of infinite direct product have finite homological dimension in <span>(X{{mathsf {-Qcoh}}})</span>. In each of the two settings, two proofs of the main result are given: a more elementary one, based on the Čech coresolution, and a more conceptual one, demonstrating existence of a generator of finite projective dimension in <span>(X{{mathsf {-Qcoh}}})</span> in the semi-separated case and using the co-contra correspondence (with contraherent cosheaves) in the Noetherian case. The hereditary complete cotorsion pair (very flat quasi-coherent sheaves, contraadjusted quasi-coherent sheaves) in the abelian category <span>(X{{mathsf {-Qcoh}}})</span> for a quasi-compact semi-separated scheme <i>X</i> is discussed.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09845-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340079","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
A Unified Characterization of Reflective Subcategories of (mathcal {Z})-closure Spaces (mathcal {Z}) -闭空间反射子范畴的统一表征
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-02-12 DOI: 10.1007/s10485-026-09848-0
Zhongxi Zhang
{"title":"A Unified Characterization of Reflective Subcategories of (mathcal {Z})-closure Spaces","authors":"Zhongxi Zhang","doi":"10.1007/s10485-026-09848-0","DOIUrl":"10.1007/s10485-026-09848-0","url":null,"abstract":"<div><p>This paper introduces and investigates the category <span>({textbf {CL}} _{mathcal {Z}})</span> of <span>(mathcal {Z})</span>-closure spaces. These spaces are defined based on a subset system <span>(mathcal {Z})</span> on the category <b>CLAT</b> of complete lattices. Specifically, a closure space X is called a <span>(mathcal {Z})</span>-closure space if its lattice of closed sets <span>(Gamma (X))</span> is closed under unions of <span>(mathcal {Z})</span>-sets (members of <span>(mathcal {Z}(Gamma (X)))</span>). We introduce the concept of <span>(mathcal {Z})</span>-irreducible sets and define an associated subset system <span>(mathcal {Z}_{I})</span> on the category <span>({textbf {CL}} _{0})</span> of <span>(T_0)</span> closure spaces. Utilizing the theory of <i>Z</i>-completions and the <i>b</i>-closure operator, we provide a complete characterization of reflective subcategories of <span>({textbf {CL}} _{mathcal {Z}})</span> that contain a specific non-<span>(T_{1})</span> space (which is pointed under certain conditions). This characterization links reflectivity to the properties of being a K-category and being equivalent to a category <span>({textbf {CCS}} _Z)</span> of <i>Z</i>-convergence <span>(mathcal {Z})</span>-closure spaces, where <i>Z</i> is a subset system coarser than <span>(mathcal {Z}_{I})</span> on <span>({textbf {CL}} _{mathcal {Z}})</span>. Furthermore, we present a unified construction for the reflective hull of subcategories within <span>({textbf {CL}} _{mathcal {Z}})</span>. Finally, we apply the main results to several concrete category instances, including closure spaces (<span>({textbf {CL}} _0)</span>), topological spaces (<span>({textbf {TOP}} _0)</span>), <i>P</i>-spaces (<span>({textbf {PTOP}} _0)</span>), convex spaces (<span>({textbf {CONV}} _0)</span>), and Alexandroff spaces (<span>({textbf {ALEX}} _0)</span>), thereby unifying and generalizing results concerning reflectivity in these categories.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338765","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
Thomason-Type Model Structures on Simplicial Complexes and Graphs 简单复合体和图上的thomason型模型结构
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-02-12 DOI: 10.1007/s10485-026-09850-6
Emilio Minichiello
{"title":"Thomason-Type Model Structures on Simplicial Complexes and Graphs","authors":"Emilio Minichiello","doi":"10.1007/s10485-026-09850-6","DOIUrl":"10.1007/s10485-026-09850-6","url":null,"abstract":"<div><p>In this paper we show that the Matsushita model structure on loop graphs, which is right-transferred from the Kan-Quillen model structure on simplicial sets, factors through two other right-transferred model structures on simplicial complexes and reflexive graphs. We show that each Quillen adjunction between these right-transferred model categories is a Quillen equivalence. These model structures are analogous to the Thomason model structure on small categories, and we prove that they are all cofibrantly generated and proper. Furthermore we show that all cofibrant simplicial complexes are flag complexes, and all forests are cofibrant.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"34 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338766","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
When is (textsf{Cat}(mathcal {Q})) Cartesian Closed? (textsf{Cat}(mathcal {Q}))何时是封闭的？
IF 0.5 4区 数学
Applied Categorical Structures Pub Date : 2026-02-01 DOI: 10.1007/s10485-026-09846-2
Isar Stubbe, Junche Yu
{"title":"When is (textsf{Cat}(mathcal {Q})) Cartesian Closed?","authors":"Isar Stubbe,&nbsp;Junche Yu","doi":"10.1007/s10485-026-09846-2","DOIUrl":"10.1007/s10485-026-09846-2","url":null,"abstract":"<div><p>We give an elementary characterization of those quantaloids <span>(mathcal {Q})</span> for which the category <span>(textsf{Cat}(mathcal {Q}))</span> of <span>(mathcal {Q})</span>-enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using <i>ad hoc</i> methods) and we give some new examples.</p></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/s10485-026-09846-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146096272","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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