{"title":"一元模型范畴中操作数的Boardman-Vogt解析","authors":"Clemens Berger , Ieke Moerdijk","doi":"10.1016/j.top.2006.05.001","DOIUrl":null,"url":null,"abstract":"<div><p>We extend the <span><math><mstyle><mi>W</mi></mstyle></math></span>-construction of Boardman and Vogt to operads of an arbitrary monoidal model category with suitable interval, and show that it provides a cofibrant resolution for well-pointed <span><math><mi>Σ</mi></math></span>-cofibrant operads. The standard simplicial resolution of Godement as well as the cobar–bar chain resolution are shown to be particular instances of this generalised <span><math><mstyle><mi>W</mi></mstyle></math></span>-construction.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 5","pages":"Pages 807-849"},"PeriodicalIF":0.0000,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.05.001","citationCount":"116","resultStr":"{\"title\":\"The Boardman–Vogt resolution of operads in monoidal model categories\",\"authors\":\"Clemens Berger , Ieke Moerdijk\",\"doi\":\"10.1016/j.top.2006.05.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We extend the <span><math><mstyle><mi>W</mi></mstyle></math></span>-construction of Boardman and Vogt to operads of an arbitrary monoidal model category with suitable interval, and show that it provides a cofibrant resolution for well-pointed <span><math><mi>Σ</mi></math></span>-cofibrant operads. The standard simplicial resolution of Godement as well as the cobar–bar chain resolution are shown to be particular instances of this generalised <span><math><mstyle><mi>W</mi></mstyle></math></span>-construction.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"45 5\",\"pages\":\"Pages 807-849\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2006.05.001\",\"citationCount\":\"116\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938306000280\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938306000280","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Boardman–Vogt resolution of operads in monoidal model categories
We extend the -construction of Boardman and Vogt to operads of an arbitrary monoidal model category with suitable interval, and show that it provides a cofibrant resolution for well-pointed -cofibrant operads. The standard simplicial resolution of Godement as well as the cobar–bar chain resolution are shown to be particular instances of this generalised -construction.
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