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Applied Categorical Structures最新文献

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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
{"title":"Higher Auslander’s defect and classifying substructures of (varvec{n})-exangulated categories","authors":"Jiangsheng Hu,&nbsp;Yajun Ma,&nbsp;Dongdong Zhang,&nbsp;Panyue Zhou","doi":"10.1007/s10485-023-09713-4","DOIUrl":"10.1007/s10485-023-09713-4","url":null,"abstract":"<div><p>Herschend–Liu–Nakaoka introduced the notion of an <i>n</i>-exangulated category. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka–Palu, but also gives a simultaneous generalization of <i>n</i>-exact categories and <span>((n+2))</span>-angulated categories. In this article, we give an <i>n</i>-exangulated version of Auslander’s defect and Auslander–Reiten duality formula. Moreover, we also give a classification of substructures (=closed subbifunctors) of a given skeletally small <i>n</i>-exangulated category by using the category of defects.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50039954","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 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,&nbsp;Anneliese Schauerte","doi":"10.1007/s10485-023-09712-5","DOIUrl":"10.1007/s10485-023-09712-5","url":null,"abstract":"<div><p>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, <span>(sigma )</span>- and <span>(kappa )</span>-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.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"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
{"title":"Closed and Open Maps for Partial Frames","authors":"J. Frith, A. Schauerte","doi":"10.1007/s10485-023-09712-5","DOIUrl":"https://doi.org/10.1007/s10485-023-09712-5","url":null,"abstract":"","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":"1-21"},"PeriodicalIF":0.6,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52044392","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
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
{"title":"Commutative Objects, Central Morphisms and Subtractors in Subtractive Categories","authors":"Vaino Tuhafeni Shaumbwa","doi":"10.1007/s10485-023-09715-2","DOIUrl":"10.1007/s10485-023-09715-2","url":null,"abstract":"<div><p>We give some characterizations of commutative objects in a subtractive category and central morphisms in a regular subtractive category. In particular, we show that commutative objects, i.e., internal unitary magmas, are the same as internal abelian groups in a subtractive category and that analogously, centrality has an alternative description in terms of so-called “subtractors” in a regular subtractive category.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09715-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45820524","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
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,&nbsp;Anthony W. Hager","doi":"10.1007/s10485-023-09710-7","DOIUrl":"10.1007/s10485-023-09710-7","url":null,"abstract":"<div><p><span>({textbf {W}})</span> denotes the category, or class of algebras, in the title. A hull operator (ho) in <span>({textbf {W}})</span> is a function <span>(textbf{ho} {textbf {W}}overset{h}{longrightarrow } {textbf {W}})</span> which can be called an essential closure operator. The family of these, denoted <span>(textbf{ho} {textbf {W}})</span>, is a proper class and a complete lattice in the ordering as functions “pointwise\", with the bottom <span>({{,textrm{Id},}}_{{textbf {W}}})</span> and top Conrad’s essential completion <i>e</i>. 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 <span>(textbf{ho} {textbf {W}})</span> through the nature of the interaction that an <i>h</i> might have with <i>B</i>, the bounded monocoreflection in <span>({textbf {W}})</span> (e.g., Bh=hB). We define and investigate three functions <span>(textbf{ho} {textbf {W}}longrightarrow textbf{ho} {textbf {W}})</span> which stand in the relation </p><div><div><span>$$begin{aligned} {{,textrm{Id},}}_{{textbf {W}}} le overline{alpha }(h) le overline{lambda }(h) le overline{c}(h) le h. end{aligned}$$</span></div></div><p>General properties that an <i>h</i> might have, and particular choices of <i>h</i>, show various assignments of &lt; and <span>(=)</span> in this chain.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"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
{"title":"Admissibility of Localizations of Crossed Modules","authors":"Olivia Monjon, J. Scherer, Florence Sterck","doi":"10.1007/s10485-023-09738-9","DOIUrl":"https://doi.org/10.1007/s10485-023-09738-9","url":null,"abstract":"","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"0 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52044402","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
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
{"title":"Descent for internal multicategory functors","authors":"Rui Prezado,&nbsp;Fernando Lucatelli Nunes","doi":"10.1007/s10485-022-09706-9","DOIUrl":"10.1007/s10485-022-09706-9","url":null,"abstract":"<div><p>We give sufficient conditions for effective descent in categories of (generalized) internal multicategories. Two approaches to study effective descent morphisms are pursued. The first one relies on establishing the category of internal multicategories as an equalizer of categories of diagrams. The second approach extends the techniques developed by Ivan Le Creurer in his study of descent for internal essentially algebraic structures.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09706-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45853869","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
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
{"title":"Trace Decategorification of Categorified Quantum sl(3)","authors":"Marko Živković","doi":"10.1007/s10485-022-09704-x","DOIUrl":"10.1007/s10485-022-09704-x","url":null,"abstract":"<div><p>We prove that the trace of categorified quantum <span>(mathfrak {sl}_3)</span> introduced by Khovanov and Lauda can also be identified with quantum <span>(mathfrak {sl}_3)</span>, thus providing an alternative way of decategorification. This is the second step of trace decategorification of quantum <span>(mathfrak {sl}_n)</span> groups over the integers, the first being the <span>(mathfrak {sl}_2)</span> case. The main technique used is decoupling of categorified quantum group into its positive and negative part. This technique can be used for more general categorified quantum groups to reduce the problem to the trace decategorification of its positive part. In the case of quantum <span>(mathfrak {sl}_3)</span>, there is an explicit form of the canonical basis of the positive (and isomorphically negative) part of it based on indecomposables found by Stošić, leading to the full result in this case.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50019537","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: 12
A symmetric approach to higher coverings in categorical Galois theory 范畴Galois理论中高覆盖的对称方法
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-01-11 DOI: 10.1007/s10485-022-09698-6
Fara Renaud, Tim Van der Linden
{"title":"A symmetric approach to higher coverings in categorical Galois theory","authors":"Fara Renaud,&nbsp;Tim Van der Linden","doi":"10.1007/s10485-022-09698-6","DOIUrl":"10.1007/s10485-022-09698-6","url":null,"abstract":"<div><p>In the context of a tower of (strongly Birkhoff) Galois structures in the sense of categorical Galois theory, we show that the concept of a higher covering admits a characterisation which is at the same time <i>absolute</i> (with respect to the base level in the tower), rather than inductively defined relative to extensions of a lower order; and <i>symmetric</i>, rather than depending on a perspective in terms of arrows pointing in a certain chosen direction. This result applies to the Galois theory of quandles, for instance, where it helps us characterising the higher coverings in purely algebraic terms.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09698-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42697676","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
Local Cohen–Macaulay DG-Modules 本地Cohen-Macaulay dg模块
IF 0.6 4区 数学
Applied Categorical Structures Pub Date : 2023-01-03 DOI: 10.1007/s10485-022-09703-y
Xiaoyan Yang, Yanjie Li
{"title":"Local Cohen–Macaulay DG-Modules","authors":"Xiaoyan Yang,&nbsp;Yanjie Li","doi":"10.1007/s10485-022-09703-y","DOIUrl":"10.1007/s10485-022-09703-y","url":null,"abstract":"<div><p>Let <i>A</i> be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal local Cohen–Macaulay DG-modules over local Cohen–Macaulay DG-rings. We also provide some characterizations of Gorenstein DG-rings by projective and injective dimensions of DG-modules.\u0000</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":"https://link.springer.com/content/pdf/10.1007/s10485-022-09703-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46569515","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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