多泛函k理论是同伦理论的等价

IF 0.7 4区数学 Q2 MATHEMATICS Journal of Homotopy and Related Structures Pub Date : 2022-11-01 DOI:10.1007/s40062-022-00317-8

Niles Johnson, Donald Yau

{"title":"多泛函k理论是同伦理论的等价","authors":"Niles Johnson, Donald Yau","doi":"10.1007/s40062-022-00317-8","DOIUrl":null,"url":null,"abstract":"<div>We show that each of the three K-theory multifunctors from small permutative categories to \\(\\mathcal {G}_*\\)-categories, \\(\\mathcal {G}_*\\)-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these K-theory multifunctors, we describe an explicit homotopy inverse functor. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann–Osorno \\(\\mathcal {E}_*\\)-categories is equivalent to the homotopy theory of pointed simplicial categories.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00317-8.pdf","citationCount":"0","resultStr":"{\"title\":\"Multifunctorial K-theory is an equivalence of homotopy theories\",\"authors\":\"Niles Johnson, Donald Yau\",\"doi\":\"10.1007/s40062-022-00317-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We show that each of the three K-theory multifunctors from small permutative categories to \\\\(\\\\mathcal {G}_*\\\\)-categories, \\\\(\\\\mathcal {G}_*\\\\)-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these K-theory multifunctors, we describe an explicit homotopy inverse functor. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann–Osorno \\\\(\\\\mathcal {E}_*\\\\)-categories is equivalent to the homotopy theory of pointed simplicial categories.</div>\",\"PeriodicalId\":49034,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40062-022-00317-8.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-022-00317-8\",\"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":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-022-00317-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了从小置换范畴到\(\mathcal {G}_*\) -范畴、\(\mathcal {G}_*\) -简单集合和连接谱的三个k理论多函子中的每一个都是同伦理论的等价。对于每一个k理论多函子，我们描述了一个显式同伦逆函子。作为我们关于点图范畴的一般结果的单独应用，我们观察到Bohmann-Osorno \(\mathcal {E}_*\) -范畴的右诱导同伦理论等价于点简单范畴的同伦理论。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Multifunctorial K-theory is an equivalence of homotopy theories

We show that each of the three K-theory multifunctors from small permutative categories to \(\mathcal {G}_*\)-categories, \(\mathcal {G}_*\)-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these K-theory multifunctors, we describe an explicit homotopy inverse functor. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann–Osorno \(\mathcal {E}_*\)-categories is equivalent to the homotopy theory of pointed simplicial categories.

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

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

期刊最新文献

Multifunctorial K-theory is an equivalence of homotopy theories Rational stabilization and maximal ideal spaces of commutative Banach algebras Homotopy Gerstenhaber algebras are strongly homotopy commutative The universal fibration with fibre X in rational homotopy theory Mapping spaces and R-completion