Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy
{"title":"通过关系限制","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":"{\"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}","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}
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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