【摘要】 以范畴逻辑与类型论为基础,引入类型中的交换群理论、环理论以及左R-模理论.证明了类型中的交换群理论在满足分配律的范畴中的模型是交换群对象,环理论的模型是环对象,左R-模理论的模型是左R-模对象,并给出左R-模理论在集合范畴和层范畴等几个具体范畴中的模型.更多还原

【Abstract】 In this paper,we introduce Abelian group theory,ring theory and left R-module theory based on Type theory.We prove that the model of Abelian group theory in Type theory is Abelian group object in category with the distributive law,ring theory is ring object,left R-module theory is left R-module object,and we give the model of left R-module in some concrete categories like Set and Sh(X).更多还原