{"title":"标量、单子和类别","authors":"Dion Coumans, B. Jacobs","doi":"10.1093/acprof:oso/9780199646296.003.0007","DOIUrl":null,"url":null,"abstract":"This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads. These interrelations will be expressed in terms of \"triangles of adjunctions\", involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"Scalars, Monads, and Categories\",\"authors\":\"Dion Coumans, B. Jacobs\",\"doi\":\"10.1093/acprof:oso/9780199646296.003.0007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads. These interrelations will be expressed in terms of \\\"triangles of adjunctions\\\", involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions.\",\"PeriodicalId\":273067,\"journal\":{\"name\":\"Quantum Physics and Linguistics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-03-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Physics and Linguistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/acprof:oso/9780199646296.003.0007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Physics and Linguistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads. These interrelations will be expressed in terms of "triangles of adjunctions", involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
