{"title":"环的自然颤动","authors":"A. Bosi, A. Facchini","doi":"10.4171/RSMUP/76","DOIUrl":null,"url":null,"abstract":"A ringed partially ordered set with zero is a pair (L,F ), where L is a partially ordered set with a least element 0L and F : L → Ring is a covariant functor. Here the partially ordered set L is given a category structure in the usual way and Ring denotes the category of associative rings with identity. Let RingedParOrd0 be the category of ringed partially ordered sets with zero. There is a functor H : Ring → RingedParOrd0 that associates to any ring R a ringed partially ordered set with zero (Hom(R), FR). The functor H has a left inverse Z : RingedParOrd0 → Ring. The category RingedParOrd0 is a fibred category. Mathematics Subject Classification (2010). Primary 18D30.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"154 1","pages":"167-180"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A natural fibration for rings\",\"authors\":\"A. Bosi, A. Facchini\",\"doi\":\"10.4171/RSMUP/76\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A ringed partially ordered set with zero is a pair (L,F ), where L is a partially ordered set with a least element 0L and F : L → Ring is a covariant functor. Here the partially ordered set L is given a category structure in the usual way and Ring denotes the category of associative rings with identity. Let RingedParOrd0 be the category of ringed partially ordered sets with zero. There is a functor H : Ring → RingedParOrd0 that associates to any ring R a ringed partially ordered set with zero (Hom(R), FR). The functor H has a left inverse Z : RingedParOrd0 → Ring. The category RingedParOrd0 is a fibred category. Mathematics Subject Classification (2010). Primary 18D30.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"154 1\",\"pages\":\"167-180\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/RSMUP/76\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/RSMUP/76","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A ringed partially ordered set with zero is a pair (L,F ), where L is a partially ordered set with a least element 0L and F : L → Ring is a covariant functor. Here the partially ordered set L is given a category structure in the usual way and Ring denotes the category of associative rings with identity. Let RingedParOrd0 be the category of ringed partially ordered sets with zero. There is a functor H : Ring → RingedParOrd0 that associates to any ring R a ringed partially ordered set with zero (Hom(R), FR). The functor H has a left inverse Z : RingedParOrd0 → Ring. The category RingedParOrd0 is a fibred category. Mathematics Subject Classification (2010). Primary 18D30.
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