{"title":"分类同伦纤维序列模型的一种新方法","authors":"Alisa Govzmann, Damjan Pivstalo, N. Poncin","doi":"10.4064/dm858-5-2022","DOIUrl":null,"url":null,"abstract":"We propose a simplified definition of Quillen’s fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding that the homotopy theory of the model category’s arrow category contains all homotopical information about its long fibration sequences. MSC 2020: 18E35, 18N40, 14A30","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A new approach to model categorical homotopy fiber sequences\",\"authors\":\"Alisa Govzmann, Damjan Pivstalo, N. Poncin\",\"doi\":\"10.4064/dm858-5-2022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a simplified definition of Quillen’s fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding that the homotopy theory of the model category’s arrow category contains all homotopical information about its long fibration sequences. MSC 2020: 18E35, 18N40, 14A30\",\"PeriodicalId\":51016,\"journal\":{\"name\":\"Dissertationes Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2021-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dissertationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/dm858-5-2022\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dissertationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/dm858-5-2022","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A new approach to model categorical homotopy fiber sequences
We propose a simplified definition of Quillen’s fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding that the homotopy theory of the model category’s arrow category contains all homotopical information about its long fibration sequences. MSC 2020: 18E35, 18N40, 14A30
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DISSERTATIONES MATHEMATICAE publishes long research papers (preferably 50-100 pages) in any area of mathematics. An important feature of papers accepted for publication should be their utility for a broad readership of specialists in the domain. In particular, the papers should be to some reasonable extent self-contained. The paper version is considered as primary.
The following criteria are taken into account in the reviewing procedure: correctness, mathematical level, mathematical novelty, utility for a broad readership of specialists in the domain, language and editorial aspects. The Editors have adopted appropriate procedures to avoid ghostwriting and guest authorship.
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