Applied Categorical Structures最新文献_第8页

Locally Type (text {FP}_{{varvec{n}}}) and ({varvec{n}})-Coherent Categories 本地输入(text {FP}_{{varvec{n}}})和({varvec{n}}) -连贯类别

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-27 DOI: 10.1007/s10485-023-09709-0

Daniel Bravo, James Gillespie, Marco A. Pérez

{"title":"Locally Type (text {FP}_{{varvec{n}}}) and ({varvec{n}})-Coherent Categories","authors":"Daniel Bravo, James Gillespie, Marco A. Pérez","doi":"10.1007/s10485-023-09709-0","DOIUrl":"10.1007/s10485-023-09709-0","url":null,"abstract":"<div>We study finiteness conditions in Grothendieck categories by introducing the concepts of objects of type (textrm{FP}_n) and studying their closure properties with respect to short exact sequences. This allows us to propose a notion of locally type (textrm{FP}_n) categories as a generalization of locally finitely generated and locally finitely presented categories. We also define and study the injective objects that are Ext-orthogonal to the class of objects of type (textrm{FP}_n), called (textrm{FP}_n)-injective objects, which will be the right half of a complete cotorsion pair. As a generalization of the category of modules over an n-coherent ring, we present the concept of n-coherent categories, which also recovers the notions of locally noetherian and locally coherent categories for (n = 0, 1). Such categories will provide a setting in which the (textrm{FP}_n)-injective cotorsion pair is hereditary, and where it is possible to construct (pre)covers by (textrm{FP}_n)-injective objects.</div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09709-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50050367","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

Locally Type $$text {FP}_{{varvec{n}}}$$ FP n and 本地键入$$text{FP}_｛varvec｛n｝｝$FP n和

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-27 DOI: 10.1007/s10485-023-09709-0

D. Bravo, James Gillespie, Marco A. Pérez

引用次数: 0

Higher Auslander’s defect and classifying substructures of (varvec{n})-exangulated categories 高等澳洲人的缺陷与(varvec{n}) -膨化分类的分类子结构

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-20 DOI: 10.1007/s10485-023-09713-4

Jiangsheng Hu, Yajun Ma, Dongdong Zhang, Panyue Zhou

引用次数: 0

Closed and Open Maps for Partial Frames 部分帧的封闭和开放映射

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-15 DOI: 10.1007/s10485-023-09712-5

John Frith, Anneliese Schauerte

{"title":"Closed and Open Maps for Partial Frames","authors":"John Frith, Anneliese Schauerte","doi":"10.1007/s10485-023-09712-5","DOIUrl":"10.1007/s10485-023-09712-5","url":null,"abstract":"<div>This paper concerns the notions of closed and open maps in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, (sigma )- and (kappa )-frames and full frames. We define closed and open maps using geometrically intuitively appealing conditions involving preservation of closed, respectively open, congruences under certain maps. We then characterize them in terms of algebraic identities involving adjoints. We note that partial frame maps need have neither right nor left adjoints whereas frame maps of course always have right adjoints. The embedding of a partial frame in either its free frame or its congruence frame has proved illuminating and useful. We consider the conditions under which these embeddings are closed, open or skeletal. We then look at preservation and reflection of closed or open maps under the functors providing the free frame or the congruence frame. Points arise naturally in the construction of the spectrum functor for partial frames to partial spaces. They may be viewed as maps from the given partial frame to the 2-chain or as certain kinds of filters; using the former description we consider closed and open points. Any point of a partial frame extends naturally to a point on its free frame and a point on its congruence frame; we consider the closedness or openness of these.</div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09712-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50029789","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

Closed and Open Maps for Partial Frames 部分帧的封闭和开放映射

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-15 DOI: 10.1007/s10485-023-09712-5

J. Frith, A. Schauerte

引用次数: 0

Commutative Objects, Central Morphisms and Subtractors in Subtractive Categories 减法范畴中的交换对象、中心态射和减法子

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-12 DOI: 10.1007/s10485-023-09715-2

Vaino Tuhafeni Shaumbwa

引用次数: 0

Some Modifications of Hull Operators in Archimedean Lattice-Ordered Groups with Weak Unit 弱单位阿基米德格序群中Hull算子的一些改进

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-02-28 DOI: 10.1007/s10485-023-09710-7

Ricardo E. Carrera, Anthony W. Hager

{"title":"Some Modifications of Hull Operators in Archimedean Lattice-Ordered Groups with Weak Unit","authors":"Ricardo E. Carrera, Anthony W. Hager","doi":"10.1007/s10485-023-09710-7","DOIUrl":"10.1007/s10485-023-09710-7","url":null,"abstract":"<div>({textbf {W}}) denotes the category, or class of algebras, in the title. A hull operator (ho) in ({textbf {W}}) is a function (textbf{ho} {textbf {W}}overset{h}{longrightarrow } {textbf {W}}) which can be called an essential closure operator. The family of these, denoted (textbf{ho} {textbf {W}}), is a proper class and a complete lattice in the ordering as functions “pointwise\", with the bottom ({{,textrm{Id},}}_{{textbf {W}}}) and top Conrad’s essential completion e. Other much studied hull operators are the divisible hull, maximum essential reflection, projectable hull, and Dedekind completion. This paper is the authors’ latest efforts to understand/create structure in (textbf{ho} {textbf {W}}) through the nature of the interaction that an h might have with B, the bounded monocoreflection in ({textbf {W}}) (e.g., Bh=hB). We define and investigate three functions (textbf{ho} {textbf {W}}longrightarrow textbf{ho} {textbf {W}}) which stand in the relation <div><div>$$begin{aligned} {{,textrm{Id},}}_{{textbf {W}}} le overline{alpha }(h) le overline{lambda }(h) le overline{c}(h) le h. end{aligned}$$</div></div>General properties that an h might have, and particular choices of h, show various assignments of < and (=) in this chain.\u0000</div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09710-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42171580","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

Admissibility of Localizations of Crossed Modules 交叉模块局部化的可接受性

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-01-20 DOI: 10.1007/s10485-023-09738-9

Olivia Monjon, J. Scherer, Florence Sterck

引用次数: 1

Descent for internal multicategory functors 内部多范畴函子的下降

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-01-17 DOI: 10.1007/s10485-022-09706-9

Rui Prezado, Fernando Lucatelli Nunes

引用次数: 1

Trace Decategorification of Categorified Quantum sl(3) 有范畴量子sl(3)的迹去范畴化

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-01-11 DOI: 10.1007/s10485-022-09704-x

Marko Živković

引用次数: 12