{"title":"同邻代数不是具体的","authors":"Ivan Di Liberti, Fosco Loregian","doi":"10.1007/s40062-018-0197-3","DOIUrl":null,"url":null,"abstract":"<p>We generalize Freyd’s well-known result that “homotopy is not concrete”, offering a general method to show that under certain assumptions on a model category <span>\\(\\mathcal {M}\\)</span>, its homotopy category <span>\\(\\textsc {ho}(\\mathcal {M})\\)</span> cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0197-3","citationCount":"1","resultStr":"{\"title\":\"Homotopical algebra is not concrete\",\"authors\":\"Ivan Di Liberti, Fosco Loregian\",\"doi\":\"10.1007/s40062-018-0197-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We generalize Freyd’s well-known result that “homotopy is not concrete”, offering a general method to show that under certain assumptions on a model category <span>\\\\(\\\\mathcal {M}\\\\)</span>, its homotopy category <span>\\\\(\\\\textsc {ho}(\\\\mathcal {M})\\\\)</span> cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-018-0197-3\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-018-0197-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-018-0197-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We generalize Freyd’s well-known result that “homotopy is not concrete”, offering a general method to show that under certain assumptions on a model category \(\mathcal {M}\), its homotopy category \(\textsc {ho}(\mathcal {M})\) cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.
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