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Journal of Homotopy and Related Structures最新文献

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Central reflections and nilpotency in exact Mal’tsev categories 马尔采夫范畴的中心反射和幂零
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-12-23 DOI: 10.1007/s40062-016-0165-8
Clemens Berger, Dominique Bourn
{"title":"Central reflections and nilpotency in exact Mal’tsev categories","authors":"Clemens Berger,&nbsp;Dominique Bourn","doi":"10.1007/s40062-016-0165-8","DOIUrl":"https://doi.org/10.1007/s40062-016-0165-8","url":null,"abstract":"<p>We study nilpotency in the context of exact Mal’tsev categories taking central extensions as the primitive notion. This yields a nilpotency tower which is analysed from the perspective of Goodwillie’s functor calculus. We show in particular that the reflection into the subcategory of <i>n</i>-nilpotent objects is the universal endofunctor of degree <i>n</i> if and only if every <i>n</i>-nilpotent object is <i>n</i>-folded. In the special context of a semi-abelian category, an object is <i>n</i>-folded precisely when its Higgins commutator of length <span>(n+1)</span> vanishes.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"765 - 835"},"PeriodicalIF":0.5,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0165-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4886371","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: 10
Étale homotopy types of moduli stacks of polarised abelian schemes Étale极化阿贝尔格式模堆的同伦类型
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-11-25 DOI: 10.1007/s40062-016-0149-8
Paola Frediani, Frank Neumann
{"title":"Étale homotopy types of moduli stacks of polarised abelian schemes","authors":"Paola Frediani,&nbsp;Frank Neumann","doi":"10.1007/s40062-016-0149-8","DOIUrl":"https://doi.org/10.1007/s40062-016-0149-8","url":null,"abstract":"<p>We determine the Artin–Mazur étale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the étale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes from an étale homotopy point of view.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"775 - 801"},"PeriodicalIF":0.5,"publicationDate":"2016-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0149-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4875310","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: 2
2-track algebras and the Adams spectral sequence 二径代数和亚当斯谱序列
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-11-24 DOI: 10.1007/s40062-016-0147-x
Hans-Joachim Baues, Martin Frankland
{"title":"2-track algebras and the Adams spectral sequence","authors":"Hans-Joachim Baues,&nbsp;Martin Frankland","doi":"10.1007/s40062-016-0147-x","DOIUrl":"https://doi.org/10.1007/s40062-016-0147-x","url":null,"abstract":"<p>In previous work of the first author and Jibladze, the <span>(E_3)</span>-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the <span>(E_3)</span>-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms <span>(E_r)</span>. In this paper, we introduce 2-track algebras and tertiary chain complexes, and we show that the <span>(E_4)</span>-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"679 - 713"},"PeriodicalIF":0.5,"publicationDate":"2016-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0147-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4945165","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
An algebraic study of the Klein Bottle 克莱因瓶的代数研究
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-11-08 DOI: 10.1007/s40062-016-0156-9
Larry A. Lambe
{"title":"An algebraic study of the Klein Bottle","authors":"Larry A. Lambe","doi":"10.1007/s40062-016-0156-9","DOIUrl":"https://doi.org/10.1007/s40062-016-0156-9","url":null,"abstract":"<p>We use symbolic computation (SC) and homological perturbation (HPT) to compute a resolution of the integers <span>(mathbb {Z})</span> over the integer group ring of <i>G</i>, the fundamental group of the Klein bottle. From this it is easy to read off the homology of the Klein bottle as well as other information.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"885 - 891"},"PeriodicalIF":0.5,"publicationDate":"2016-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0156-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4358842","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
Coherence and strictification for self-similarity 自相似的一致性和严格性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-11-07 DOI: 10.1007/s40062-016-0154-y
Peter Hines
{"title":"Coherence and strictification for self-similarity","authors":"Peter Hines","doi":"10.1007/s40062-016-0154-y","DOIUrl":"https://doi.org/10.1007/s40062-016-0154-y","url":null,"abstract":"<p>This paper studies questions of coherence and strictification related to self-similarity—the identity <span>(Scong Sotimes S)</span> in a semi-monoidal category. Based on Saavedra’s theory of units, we first demonstrate that strict self-similarity cannot simultaneously occur with strict associativity—i.e. no monoid may have a strictly associative (semi-) monoidal tensor, although many monoids have a semi-monoidal tensor associative up to isomorphism. We then give a simple coherence result for the arrows exhibiting self-similarity and use this to describe a ‘strictification procedure’ that gives a semi-monoidal equivalence of categories relating strict and non-strict self-similarity, and hence monoid analogues of many categorical properties. Using this, we characterise a class of diagrams (built from the canonical isomorphisms for the relevant tensors, together with the isomorphisms exhibiting the self-similarity) that are guaranteed to commute, and give a simple intuitive interpretation of this characterisation.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"847 - 867"},"PeriodicalIF":0.5,"publicationDate":"2016-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0154-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4636362","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: 11
Computing Bredon homology of groups 群的Bredon同调计算
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-11-04 DOI: 10.1007/s40062-016-0146-y
A. T. Bui, Graham Ellis
{"title":"Computing Bredon homology of groups","authors":"A. T. Bui,&nbsp;Graham Ellis","doi":"10.1007/s40062-016-0146-y","DOIUrl":"https://doi.org/10.1007/s40062-016-0146-y","url":null,"abstract":"<p>We describe the basic ingredients of a general computational framework for performing machine calculations in the cohomology of groups. This has been implemented in the <span>GAP</span> system for computational algebra and the paper is intended to aid those wishing to extend that implementation to their own needs.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"715 - 734"},"PeriodicalIF":0.5,"publicationDate":"2016-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0146-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4516448","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: 2
Homotopy colimits of 2-functors 2函子的同伦极限
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-10-31 DOI: 10.1007/s40062-016-0150-2
A. M. Cegarra, B. A. Heredia
{"title":"Homotopy colimits of 2-functors","authors":"A. M. Cegarra,&nbsp;B. A. Heredia","doi":"10.1007/s40062-016-0150-2","DOIUrl":"https://doi.org/10.1007/s40062-016-0150-2","url":null,"abstract":"<p>Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend lower categorical analogues that have been classically used in algebraic topology and algebraic K-theory, such as the homotopy invariance theorem (by Bousfield and Kan), the homotopy colimit theorem (Thomason), Theorems A and B (Quillen), or the homotopy cofinality theorem (Hirschhorn).</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"735 - 774"},"PeriodicalIF":0.5,"publicationDate":"2016-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0150-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5186655","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
Special volume dedicated to Ronald Brown for his 80th birthday 献给罗纳德·布朗80岁生日的特别卷
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-10-27 DOI: 10.1007/s40062-016-0151-1
Maria Manuel Clementino, Marino Gran, George Janelidze, Timothy Porter
{"title":"Special volume dedicated to Ronald Brown for his 80th birthday","authors":"Maria Manuel Clementino,&nbsp;Marino Gran,&nbsp;George Janelidze,&nbsp;Timothy Porter","doi":"10.1007/s40062-016-0151-1","DOIUrl":"https://doi.org/10.1007/s40062-016-0151-1","url":null,"abstract":"","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"631 - 642"},"PeriodicalIF":0.5,"publicationDate":"2016-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0151-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5056085","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
A bigroupoid’s topology (or, Topologising the homotopy bigroupoid of a space) 一个双群拟体的拓扑(或对空间的同伦双群拟体进行拓扑化)
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-10-26 DOI: 10.1007/s40062-016-0160-0
David Michael Roberts
{"title":"A bigroupoid’s topology (or, Topologising the homotopy bigroupoid of a space)","authors":"David Michael Roberts","doi":"10.1007/s40062-016-0160-0","DOIUrl":"https://doi.org/10.1007/s40062-016-0160-0","url":null,"abstract":"<p>The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown and Danesh-Naruie lifted the fundamental groupoid to a topological groupoid. For locally relatively contractible spaces the resulting topological bigroupoid is <i>locally trivial</i> in a way analogous to the case of the topologised fundamental groupoid. This is the published version of arXiv:1302.7019.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"923 - 942"},"PeriodicalIF":0.5,"publicationDate":"2016-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0160-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5021367","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
The category of equilogical spaces and the effective topos as homotopical quotients 等价空间的范畴与同调商的有效拓扑
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2016-10-25 DOI: 10.1007/s40062-016-0161-z
Giuseppe Rosolini
{"title":"The category of equilogical spaces and the effective topos as homotopical quotients","authors":"Giuseppe Rosolini","doi":"10.1007/s40062-016-0161-z","DOIUrl":"https://doi.org/10.1007/s40062-016-0161-z","url":null,"abstract":"<p>We show that the two models of an extensional version of Martin-L?f type theory, those given by the category of equilogical spaces and by the effective topos, are homotopical quotients of appropriate categories of 2-groupoids.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"943 - 956"},"PeriodicalIF":0.5,"publicationDate":"2016-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0161-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4984367","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: 4
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