{"title":"共同生成的模型类别的超类别和下类别","authors":"Philip S. Hirschhorn","doi":"10.1007/s40062-021-00294-4","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span>\\(\\mathcal {M}\\)</span> be a model category and let <i>Z</i> be an object of <span>\\(\\mathcal {M}\\)</span>. We show that if <span>\\(\\mathcal {M}\\)</span> is cofibrantly generated, cellular, left proper, or right proper, then both the model category <img> of objects of <span>\\(\\mathcal {M}\\)</span> over <i>Z</i> and the model category <img> of objects of <span>\\(\\mathcal {M}\\)</span> under <i>Z</i> are as well.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Overcategories and undercategories of cofibrantly generated model categories\",\"authors\":\"Philip S. Hirschhorn\",\"doi\":\"10.1007/s40062-021-00294-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span>\\\\(\\\\mathcal {M}\\\\)</span> be a model category and let <i>Z</i> be an object of <span>\\\\(\\\\mathcal {M}\\\\)</span>. We show that if <span>\\\\(\\\\mathcal {M}\\\\)</span> is cofibrantly generated, cellular, left proper, or right proper, then both the model category <img> of objects of <span>\\\\(\\\\mathcal {M}\\\\)</span> over <i>Z</i> and the model category <img> of objects of <span>\\\\(\\\\mathcal {M}\\\\)</span> under <i>Z</i> are as well.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-10-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-021-00294-4\",\"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/s40062-021-00294-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Overcategories and undercategories of cofibrantly generated model categories
Let \(\mathcal {M}\) be a model category and let Z be an object of \(\mathcal {M}\). We show that if \(\mathcal {M}\) is cofibrantly generated, cellular, left proper, or right proper, then both the model category of objects of \(\mathcal {M}\) over Z and the model category of objects of \(\mathcal {M}\) under Z are as well.
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