{"title":"EQ-代数的范畴","authors":"R. Borzooei, N. Akhlaghinia, M. Kologani, X. Xin","doi":"10.18778/0138-0680.2021.01","DOIUrl":null,"url":null,"abstract":"\n \n \nEQ-algebras were introduced by Nova ́k in [15] as an algebraic structure of truth values for fuzzy type theory (FFT). In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculate coprodut and pushout in a special case. Also, we construct a free EQ-algebra on a singleton. \n \n \n","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The category of EQ-algebras\",\"authors\":\"R. Borzooei, N. Akhlaghinia, M. Kologani, X. Xin\",\"doi\":\"10.18778/0138-0680.2021.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n \\n \\nEQ-algebras were introduced by Nova ́k in [15] as an algebraic structure of truth values for fuzzy type theory (FFT). In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculate coprodut and pushout in a special case. Also, we construct a free EQ-algebra on a singleton. \\n \\n \\n\",\"PeriodicalId\":38667,\"journal\":{\"name\":\"Bulletin of the Section of Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Section of Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18778/0138-0680.2021.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Section of Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18778/0138-0680.2021.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
EQ-algebras were introduced by Nova ́k in [15] as an algebraic structure of truth values for fuzzy type theory (FFT). In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculate coprodut and pushout in a special case. Also, we construct a free EQ-algebra on a singleton.
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