{"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":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 3","pages":"673 - 687"},"PeriodicalIF":0.5000,"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\":49034,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"13 3\",\"pages\":\"673 - 687\"},\"PeriodicalIF\":0.5000,\"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\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-018-0197-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-018-0197-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences.
Journal of Homotopy and Related Structures is intended to publish papers on
Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
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