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

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.