{"title":"组合模型类别等同于可呈现的准类别","authors":"Dmitri Pavlov","doi":"10.1016/j.jpaa.2024.107860","DOIUrl":null,"url":null,"abstract":"<div><div>We establish a Dwyer–Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable <span><math><mo>(</mo><mi>∞</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories. This implies that the underlying quasicategories of these relative categories are also equivalent. This article is also available at <span><span>arXiv:2110.04679v3</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107860"},"PeriodicalIF":0.7000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combinatorial model categories are equivalent to presentable quasicategories\",\"authors\":\"Dmitri Pavlov\",\"doi\":\"10.1016/j.jpaa.2024.107860\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We establish a Dwyer–Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable <span><math><mo>(</mo><mi>∞</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories. This implies that the underlying quasicategories of these relative categories are also equivalent. This article is also available at <span><span>arXiv:2110.04679v3</span><svg><path></path></svg></span>.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 2\",\"pages\":\"Article 107860\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404924002573\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/6 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924002573","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/6 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Combinatorial model categories are equivalent to presentable quasicategories
We establish a Dwyer–Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable -categories. This implies that the underlying quasicategories of these relative categories are also equivalent. This article is also available at arXiv:2110.04679v3.
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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