{"title":"类型理论和均匀纤维的克里普克-乔亚尔强制力","authors":"Steve Awodey, Nicola Gambino, Sina Hazratpour","doi":"10.1007/s00029-024-00962-2","DOIUrl":null,"url":null,"abstract":"<p>We introduce a new method for precisely relating algebraic structures in a presheaf category and judgements of its internal type theory. The method provides a systematic way to organise complex diagrammatic reasoning and generalises the well-known Kripke-Joyal forcing for logic. As an application, we prove several properties of algebraic weak factorisation systems considered in Homotopy Type Theory.\n</p>","PeriodicalId":501600,"journal":{"name":"Selecta Mathematica","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kripke-Joyal forcing for type theory and uniform fibrations\",\"authors\":\"Steve Awodey, Nicola Gambino, Sina Hazratpour\",\"doi\":\"10.1007/s00029-024-00962-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce a new method for precisely relating algebraic structures in a presheaf category and judgements of its internal type theory. The method provides a systematic way to organise complex diagrammatic reasoning and generalises the well-known Kripke-Joyal forcing for logic. As an application, we prove several properties of algebraic weak factorisation systems considered in Homotopy Type Theory.\\n</p>\",\"PeriodicalId\":501600,\"journal\":{\"name\":\"Selecta Mathematica\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Selecta Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00029-024-00962-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Selecta Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00029-024-00962-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Kripke-Joyal forcing for type theory and uniform fibrations
We introduce a new method for precisely relating algebraic structures in a presheaf category and judgements of its internal type theory. The method provides a systematic way to organise complex diagrammatic reasoning and generalises the well-known Kripke-Joyal forcing for logic. As an application, we prove several properties of algebraic weak factorisation systems considered in Homotopy Type Theory.
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