Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy
{"title":"Limits via relations","authors":"Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy","doi":"arxiv-2405.03175","DOIUrl":null,"url":null,"abstract":"In this paper, we study operations on functors in the category of abelian\ngroups simplar to the derivation in the sense of Dold-Puppe. They are defined\nas derived limits of a functor applied to the relation subgroup over a category\nof free presentations of the group. The integral homology of the\nEilenberg-Maclane space $K(\\mathbb Z,3)$ appears as a part of description of\nthese operations applied to symmetric powers.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"2012 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-06","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-2405.03175","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study operations on functors in the category of abelian
groups simplar to the derivation in the sense of Dold-Puppe. They are defined
as derived limits of a functor applied to the relation subgroup over a category
of free presentations of the group. The integral homology of the
Eilenberg-Maclane space $K(\mathbb Z,3)$ appears as a part of description of
these operations applied to symmetric powers.
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