Riesz模范畴的完备性和余完备性  

Completeness and Cocompleteness of the Category of Riesz Modules

作　　者：李丹阳 汤建钢 LI Dan-yang;TANG Jian-gang(College of Mathematics and Statistics,Yili Normal University,Yining,Xinjiang,835000,China;Institute of Applied Mathematics,Yili Normal University,Yining,Xinjiang,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 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《新疆师范大学学报（自然科学版）》2024年第1期13-21,共9页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：伊犁师范大学提升学科综合实力专项项目(22XKZZ20)。

摘　　要：范畴论是现代数学的基础,从Riesz模范畴出发,研究Riesz模的内部特征是研究Riesz模的重要方法。范畴的极限是范畴论的重要概念之一,范畴中乘积、等值子概念均可以看作是范畴的某种特殊的极限,余积、余等值子是特殊的余极限。范畴中极限的存在性决定了该范畴的完备性,余极限的存在性决定了余完备性。通过对以Riesz模为对象,Riesz模同态为态射的Riesz模范畴极限的研究,给出了Riesz模范畴中的乘积与余积、等值子与余等值子的具体表示形式,进而证明了Riesz模范畴具有完备性和余完备性。Category theory is the foundation of modern mathematics.Starting from the category of Riesz modules,the study of the internal characteristics of Riesz modules is an important method for studying Riesz modules.The limit of a category is one of the key concepts of category theory.The concepts of product and equalizer in the category can all be seen as some kind of special limit of the category,and the coproduct and coequalizer are special colimits.The existence of a limit in the category determines the completeness of the category,and the existence of a colimit determines cocompleteness.Specific representations of product and coproduct,equalizer and coequalizer in the category of Riesz modules are given by studying the limits of the category of Riesz modules with Riesz modules as objects and Riesz modules homomorphisms as morphisms,which in turn prove that the category of Riesz modules has completeness and cocompleteness.

关 键 词：Riesz模 范畴 等值子 余等值子 完备性 余完备性 

分 类 号：O153.1[理学—数学] O153.3[理学—基础数学]