Applied Categorical Structures最新文献_第6页

Generalization of the Dehornoy–Lafont Order Complex to Categories: Application to Exceptional Braid Groups 德霍诺伊-拉丰阶复数在范畴中的泛化：特殊辫状群的应用

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-12-12 DOI: 10.1007/s10485-023-09757-6

Owen Garnier

引用次数: 0

Koszul Monoids in Quasi-abelian Categories 准阿贝尔范畴中的科斯祖尔单体

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-12-06 DOI: 10.1007/s10485-023-09756-7

Rhiannon Savage

引用次数: 0

Homotopy Sheaves on Generalised Spaces 广义空间上的同伦轴

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-12-04 DOI: 10.1007/s10485-023-09754-9

Severin Bunk

{"title":"Homotopy Sheaves on Generalised Spaces","authors":"Severin Bunk","doi":"10.1007/s10485-023-09754-9","DOIUrl":"10.1007/s10485-023-09754-9","url":null,"abstract":"<div><p>We study the homotopy right Kan extension of homotopy sheaves on a category to its free cocompletion, i.e. to its category of presheaves. Any pretopology on the original category induces a canonical pretopology of generalised coverings on the free cocompletion. We show that with respect to these pretopologies the homotopy right Kan extension along the Yoneda embedding preserves homotopy sheaves valued in (sufficiently nice) simplicial model categories. Moreover, we show that this induces an equivalence between sheaves of spaces on the original category and colimit-preserving sheaves of spaces on its free cocompletion. We present three applications in geometry and topology: first, we prove that diffeological vector bundles descend along subductions of diffeological spaces. Second, we deduce that various flavours of bundle gerbes with connection satisfy <span>((infty ,2))</span>-categorical descent. Finally, we investigate smooth diffeomorphism actions in smooth bordism-type field theories on a manifold. We show how these smooth actions allow us to extract the values of a field theory on any object coherently from its values on generating objects of the bordism category.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 6","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09754-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138485110","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

Unbounded Algebraic Derivators 无界代数导数

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-12-02 DOI: 10.1007/s10485-023-09752-x

Leovigildo Alonso Tarrío, Beatriz Álvarez Díaz, Ana Jeremías López

引用次数: 0

Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories 一般组合模型范畴中经由同伦末端的同伦极限

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-11-27 DOI: 10.1007/s10485-023-09747-8

Sergey Arkhipov, Sebastian Ørsted

引用次数: 5

Partialising Institutions Partialising机构

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-11-15 DOI: 10.1007/s10485-023-09753-w

Răzvan Diaconescu

引用次数: 0

Compact Hausdorff Locales in Presheaf Toposes Presheaf拓扑中的紧凑Hausdorff区域

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-10-19 DOI: 10.1007/s10485-023-09751-y

Simon Henry, Christopher Townsend

引用次数: 1

Continuous Nakayama Representations 连续中山表示

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-10-03 DOI: 10.1007/s10485-023-09748-7

Job Daisie Rock, Shijie Zhu

引用次数: 0

Pervin Spaces and Frith Frames: Bitopological Aspects and Completion Pervin空间与Frith框架：双拓扑方面与完成

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-09-30 DOI: 10.1007/s10485-023-09749-6

Célia Borlido, Anna Laura Suarez

{"title":"Pervin Spaces and Frith Frames: Bitopological Aspects and Completion","authors":"Célia Borlido, Anna Laura Suarez","doi":"10.1007/s10485-023-09749-6","DOIUrl":"10.1007/s10485-023-09749-6","url":null,"abstract":"<div><p>A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames, and that the latter may be seen as representatives of certain quasi-uniform structures. As such, they have an underlying bitopological structure and inherit a natural notion of completion. In this paper we start by exploring the bitopological nature of Pervin spaces and of Frith frames, proving some categorical equivalences involving zero-dimensional structures. We then provide a conceptual proof of a duality between the categories of <span>(T_0)</span> complete Pervin spaces and of complete Frith frames. This enables us to interpret several Stone-type dualities as a restriction of the dual adjunction between Pervin spaces and Frith frames along full subcategory embeddings. Finally, we provide analogues of Banaschewski and Pultr’s characterizations of sober and <span>(T_D)</span> topological spaces in the setting of Pervin spaces and of Frith frames, highlighting the parallelism between the two notions.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09749-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50055551","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

From Gs-monoidal to Oplax Cartesian Categories: Constructions and Functorial Completeness 从gs -一元到Oplax笛卡尔范畴:构造与功能完备性

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-09-28 DOI: 10.1007/s10485-023-09750-z

Tobias Fritz, Fabio Gadducci, Davide Trotta, Andrea Corradini

引用次数: 1