{"title":"亲范畴上的简单模型结构","authors":"Thomas Blom, Ieke Moerdijk","doi":"10.2140/agt.2023.23.3849","DOIUrl":null,"url":null,"abstract":"We describe a method for constructing simplicial model structures on ind- and pro-categories. Our method is particularly useful for constructing analogues of known model categories. Our construction quickly recovers Morel's model structure for pro-p spaces and Quick's model structure for profinite spaces, but we will show that it can also be applied to construct many interesting new model structures. In addition, we study some general properties of our method, such as its functorial behaviour and its relation to Bousfield localization. We compare our construction to the infinity-categorical approach to ind- and pro-categories in an appendix.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"38 2","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Simplicial model structures on pro-categories\",\"authors\":\"Thomas Blom, Ieke Moerdijk\",\"doi\":\"10.2140/agt.2023.23.3849\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe a method for constructing simplicial model structures on ind- and pro-categories. Our method is particularly useful for constructing analogues of known model categories. Our construction quickly recovers Morel's model structure for pro-p spaces and Quick's model structure for profinite spaces, but we will show that it can also be applied to construct many interesting new model structures. In addition, we study some general properties of our method, such as its functorial behaviour and its relation to Bousfield localization. We compare our construction to the infinity-categorical approach to ind- and pro-categories in an appendix.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"38 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2023.23.3849\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.3849","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We describe a method for constructing simplicial model structures on ind- and pro-categories. Our method is particularly useful for constructing analogues of known model categories. Our construction quickly recovers Morel's model structure for pro-p spaces and Quick's model structure for profinite spaces, but we will show that it can also be applied to construct many interesting new model structures. In addition, we study some general properties of our method, such as its functorial behaviour and its relation to Bousfield localization. We compare our construction to the infinity-categorical approach to ind- and pro-categories in an appendix.