{"title":"关于群-2-类群的进一步说明","authors":"Sedat Temel","doi":"10.4995/AGT.2021.13148","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to obtain a group-2-groupoid as a 2-groupoid object in the category of groups and also as a special kind of an internal category in the category of group-groupoids. Corresponding group2-groupoids, we obtain some categorical structures related to crossed modules and group-groupoids and prove categorical equivalences between them. These results enable us to obtain 2-dimensional notions of group-groupoids. 2010 MSC: 20L05; 18D05; 18D35; 20J15.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"18 1","pages":"31"},"PeriodicalIF":0.6000,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Further remarks on group-2-groupoids\",\"authors\":\"Sedat Temel\",\"doi\":\"10.4995/AGT.2021.13148\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to obtain a group-2-groupoid as a 2-groupoid object in the category of groups and also as a special kind of an internal category in the category of group-groupoids. Corresponding group2-groupoids, we obtain some categorical structures related to crossed modules and group-groupoids and prove categorical equivalences between them. These results enable us to obtain 2-dimensional notions of group-groupoids. 2010 MSC: 20L05; 18D05; 18D35; 20J15.\",\"PeriodicalId\":8046,\"journal\":{\"name\":\"Applied general topology\",\"volume\":\"18 1\",\"pages\":\"31\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied general topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4995/AGT.2021.13148\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied general topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4995/AGT.2021.13148","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The aim of this paper is to obtain a group-2-groupoid as a 2-groupoid object in the category of groups and also as a special kind of an internal category in the category of group-groupoids. Corresponding group2-groupoids, we obtain some categorical structures related to crossed modules and group-groupoids and prove categorical equivalences between them. These results enable us to obtain 2-dimensional notions of group-groupoids. 2010 MSC: 20L05; 18D05; 18D35; 20J15.
期刊介绍：
The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.
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