关于分式S-系的一个注记  

A note on fractional S-acts

作　　者：梁星亮[1,2] 李宇航 Xingliang LIANG;Yuhang LI(School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710021,Shaanxi,China;School of Mathematics,Northwest University,Xi'an 710127,Shaanxi,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021 [2]西北大学数学学院,陕西西安710127

出　　处：《山东大学学报（理学版）》2024年第8期1-8,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12001345);中国博士后科学基金资助项目(2020M673618XB)。

摘　　要：设S是交换幺半群,在S-系范畴中,借助拉回图的映射的单、满性,给出了分式函子(S-系范畴到分式S-系范畴)保持平坦性质的一个新证明,研究了分式函子与有向上极限之间的关系,给出了分式S-系具有覆盖的一个充分条件。Let S be a commutative monoid,in the category of S-acts,by the injectivity and surjectivity of the mapping of pullback diagrams,a new proof that fractional functors(the category of S-acts to the category of fractional S-acts)preserve flatness properties is given.The relationship between fractional functors and directed colimits is investigated.A sufficient condition for fractional S-acts having a cover is presented.

关 键 词：交换幺半群 S-系 拉回图 平坦性质 有向上极限 

分 类 号：O152.7[理学—数学]