{"title":"布斯菲尔德-坎${/mathbb{Q}}$补全和${mathbb{Q}}$良好空间的列特性分析","authors":"Yves Félix, Mario Fuentes, Aniceto Murillo","doi":"arxiv-2407.02812","DOIUrl":null,"url":null,"abstract":"We prove that the unit of the Quillen pair ${\\mathfrak{L}}\\colon {\\bf\nsset}\\rightleftarrows {\\bf cdgl}\\colon {\\langle\\,\\cdot\\,\\rangle}$ given by the\nmodel and realization functor is, up to homotopy, the Bousfield-Kan\n${\\mathbb{Q}}$-completion.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Lie characterization of the Bousfield-Kan ${\\\\mathbb{Q}}$-completion and ${\\\\mathbb{Q}}$-good spaces\",\"authors\":\"Yves Félix, Mario Fuentes, Aniceto Murillo\",\"doi\":\"arxiv-2407.02812\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the unit of the Quillen pair ${\\\\mathfrak{L}}\\\\colon {\\\\bf\\nsset}\\\\rightleftarrows {\\\\bf cdgl}\\\\colon {\\\\langle\\\\,\\\\cdot\\\\,\\\\rangle}$ given by the\\nmodel and realization functor is, up to homotopy, the Bousfield-Kan\\n${\\\\mathbb{Q}}$-completion.\",\"PeriodicalId\":501119,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Topology\",\"volume\":\"34 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.02812\",\"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 - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.02812","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Lie characterization of the Bousfield-Kan ${\mathbb{Q}}$-completion and ${\mathbb{Q}}$-good spaces
We prove that the unit of the Quillen pair ${\mathfrak{L}}\colon {\bf
sset}\rightleftarrows {\bf cdgl}\colon {\langle\,\cdot\,\rangle}$ given by the
model and realization functor is, up to homotopy, the Bousfield-Kan
${\mathbb{Q}}$-completion.
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