内蕴左R-模范畴在Ω-集范畴中的表示  

Representation of the Category of Internal Left R-module Objects in the Category of Ω-sets

作　　者：徐亚琴 汤建钢 XU Ya-qin;TANG Jian-gang(College of Mathematics and statistics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新刺伊宁835000

出　　处：《模糊系统与数学》2021年第2期18-31,共14页Fuzzy Systems and Mathematics

基　　金：自治区高校科研计划项目;伊犁师范大学2020年度研究生科研创新项目(XJ2020G300)。

摘　　要：本文研究内蕴环范畴在集合范畴中的表示,内蕴Abel群范畴在集合范畴中的表示,以及内蕴左R-模范畴在集合范畴中的表示,进一步,研究内蕴左R-模范畴在Ω-集范畴中的表示,给出基于Ω-集范畴的内蕴左R-模范畴与Ω-左R-模范畴之间的同构关系。In this paper, we study properties of the category of internal ring objects, the category of internal Abelian group objects and the category of internal left R-model objects in a category with finite product and distributive law, representation of the three internal categories in the category of sets is studied respectively, further more the representation of the category of internal left R-module objects in the category of Ω-sets is investigated, and the isomorphic relation between the category of internal left R-module objects in the category of Ω-sets and the category of Ω-left R-modules is given.

关 键 词：内蕴Abel群范畴 内蕴环范畴 内蕴左R-模范畴 Ω-左R-模范畴 表示定理 

分 类 号：O154[理学—数学] O159[理学—基础数学]