内蕴Abel群范畴在Ω-集范畴中的表示  

Representation of the Category of Internal Abelian Group 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,新疆伊宁835000

出　　处：《数学的实践与认识》2021年第12期232-244,共13页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU20191024)。

摘　　要：在具有有限乘积的范畴中讨论内蕴Abel群范畴的性质,研究内蕴Abel群范畴在集合范畴中的表示,进一步,研究内蕴Abel群范畴在Ω-集范畴中的表示,给出基于Ω-集范畴的内蕴Abel群范畴与Ω-Abel群范畴之间的同构关系.In this paper,we discuss some properties of the category of internal Abelian group objects in a category with finite product,the representation theorem of the category of internal Abelian group objects in the category of sets is studied,further more,the representation of the category of internal Abelian group objects in the category of Ω-sets is investigated,and the isomorphic relation between the category of internal Abelian group objects in the category of Ω-sets and the category of Ω-Abelian groups is given.

关 键 词：内蕴Abel群 Ω-集 Ω-Abel群 范畴 表示 

分 类 号：O154.1[理学—数学]