通过 $\infty$-category 动作完成分组

arXiv - MATH - K-Theory and Homology Pub Date : 2024-05-20 DOI:arxiv-2405.12118

Georg Lehner

{"title":"通过 $\\infty$-category 动作完成分组","authors":"Georg Lehner","doi":"arxiv-2405.12118","DOIUrl":null,"url":null,"abstract":"We give a generalization of Quillen's $S^{-1}S$ construction for arbitrary\n$E_n$-monoids as an $E_{n-1}$-monoidal $\\infty$-category and show that its\nrealization models the group completion provided that $n \\geq 2$. We will also\nshow how this construction is related to a variety of other constructions of\nthe group completion.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Group completion via the action $\\\\infty$-category\",\"authors\":\"Georg Lehner\",\"doi\":\"arxiv-2405.12118\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a generalization of Quillen's $S^{-1}S$ construction for arbitrary\\n$E_n$-monoids as an $E_{n-1}$-monoidal $\\\\infty$-category and show that its\\nrealization models the group completion provided that $n \\\\geq 2$. We will also\\nshow how this construction is related to a variety of other constructions of\\nthe group completion.\",\"PeriodicalId\":501143,\"journal\":{\"name\":\"arXiv - MATH - K-Theory and Homology\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2405.12118\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.12118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们给出了奎林对任意$E_n$单元的$S^{-1}S$构造作为$E_{n-1}$单元$\infty$类别的广义化，并证明只要$n \geq 2$，它的实现就是群完成的模型。我们还将展示这一构造与群完形的其他各种构造之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Group completion via the action $\infty$-category

We give a generalization of Quillen's $S^{-1}S$ construction for arbitrary $E_n$-monoids as an $E_{n-1}$-monoidal $\infty$-category and show that its realization models the group completion provided that $n \geq 2$. We will also show how this construction is related to a variety of other constructions of the group completion.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - K-Theory and Homology

自引率

0.00%

发文量