Riesz模范畴中拉回与推出的性质研究

Study on Properties of Pull-back and Push-out in the Category of Riesz Modules

拉回和推出也称为纤维积和纤维余积,是范畴论中两个重要的对偶概念,属于数学中诸多概念的抽象,具有丰富的内涵。文章在Riesz模范畴中研究拉回与推出的存在性和唯一性。首先引入拉回的概念,构造出满足Riesz模范畴中拉回概念的一个对象和一对态射,并证明拉回的存在性和唯一性;对偶地,在Riesz模范畴中引入同余关系的概念,在此基础上,运用同余关系作商,定义出了Riesz模的商的概念,再对推出的概念进行定义,构造出满足Riesz模范畴中推出概念的一个对象和一对态射,并证明推出的存在性和唯一性。

ion of many concepts in mathematics,with rich connotations.In this paper,existence and uniqueness of pull-back and push-out are studied in the category of Riesz modules.Firstly the notion of pull-back is introduced by constructing an object and a pair of morphisms that satisfy the notion of pull-back in the category of Riesz modules,and prove the existence and uniqueness of pull-back.Dually,the notion of congruence relation is introduced in the category of Riesz modules,based on which the notion of quotient of Riesz modules is defined by applying the congruence relation as a quotient.Then,the notion of push-out is defined by constructing an object and a pair of morphisms that satisfy the notion of push-out in the category of Riesz modules,and prove the existence and uniqueness of push-out.