{"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><p>We show that each of the three <i>K</i>-theory multifunctors from small permutative categories to <span>\\(\\mathcal {G}_*\\)</span>-categories, <span>\\(\\mathcal {G}_*\\)</span>-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these <i>K</i>-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 <span>\\(\\mathcal {E}_*\\)</span>-categories is equivalent to the homotopy theory of pointed simplicial categories.</p></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}
引用次数: 0
Abstract
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
