范畴与半群  

Categories and Semigroups

作　　者：喻秉钧 YU Bingjun(College of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2022年第2期143-159,F0002,共18页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10871161)。

摘　　要：利用范畴中态射的左右可消、左右可逆等不同性质,逐层次地定义有像范畴、幂富范畴和平衡范畴,通过研究这几类范畴与其锥半群内在性质的相互关系,证明它们分别刻画了左富足半群和富足半群的结构.作为推论,还从范畴角度刻画幂等元生成正则子半群的富足半群,从而把Nambooripad(Theory of Cross-connections[M].Trivandrum:Centre for Mathematical Sciences,1994.)用正规范畴刻画正则半群结构的理论推广到富足半群以至左富足半群.In this paper,by using the left,right cancelable and reversible properties of morphisms in a category,the concepts of categories with images,idempotent ample categories and balanced categories are introduced step by step.The intrinsic relationship between these categories and their cone semigroups are investigated.It is proved that the cone semigroup of an idempotent ample category is left abundant and vise versa,the principal left*-ideal category of a left(not necessarily right)abundant semigroup is an idempotent ample category.Similar result holds for balanced categories and abundant semigroups.As a consequence,an abundant semigroup whose regular elements form a regular subsemigroup is characterized in terms of category.Therefore,the significant theory of normal categories and regular semigroups due to KSS,Nambooripad is generalized to left abundant semigroups and abundant semigroups,respectively.

关 键 词：有像范畴 幂富范畴 平衡范畴 锥及其平衡表示 有像范畴的锥半群 (规范)左(右)富足半群 富足(正则)半群 

分 类 号：O152.7[理学—数学]