{"title":"利用同伦相干神经对空间进行分类","authors":"Kensuke Arakawa","doi":"10.4310/hha.2023.v25.n2.a16","DOIUrl":null,"url":null,"abstract":"We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve. We will also show that the claim remains valid for simplicial groupoids.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":"12 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classifying space via homotopy coherent nerve\",\"authors\":\"Kensuke Arakawa\",\"doi\":\"10.4310/hha.2023.v25.n2.a16\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve. We will also show that the claim remains valid for simplicial groupoids.\",\"PeriodicalId\":55050,\"journal\":{\"name\":\"Homology Homotopy and Applications\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Homology Homotopy and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/hha.2023.v25.n2.a16\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Homology Homotopy and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/hha.2023.v25.n2.a16","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve. We will also show that the claim remains valid for simplicial groupoids.
期刊介绍：
Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.
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