对合Quantale范畴中的自由对象及其良幂性  

The Free Objects in the Category of Involutive Quantales and its Property of Well-powered

作　　者：周异辉[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2006年第2期216-224,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10471083);教育部"高校青年教师奖"基金(教人司[2000]26号)

摘　　要：本文首先给出了对合Quantale余核映射的概念,证明了任意子对合Quantale都是某对合Quantale余核映射的象。其次构造出了对合Quantale范畴IQuant中由集合生成的自由对合Quantale的具体结构,证明了遗忘函子 U:IQuant→Set有左伴随,并给出了其左伴随函子。最后,证明了IQuant中的单态射恰为单同态,得出了对合Quantale上的余核映射与其在范畴IQuant 中的子对象是一一对应的,从而证明了IQuant是良幂的。First, the concept of involutive quantic conucleus is given, and it is proved that every sub-involutive quantale is the image of some involutive quantic conucleus. Second, the free involutive quantale generated by a set is constructed and hence the forgetful functor U： IQuant→ Set has a given left adjoint. At last, we proved that the monomorphism in IQuant is precisely the injective homomorphism. And a one-to-one correspondence between the set of all the involutive quantic conucleus on a involutive quantale and the set of all the sub-objects of it in IQuant can be obtained. So, the well-powered fact of IQuant is proved.

关 键 词：对合QUANTALE 对合Quantale余核映射 自由对象 伴随函子 

分 类 号：O153.1[理学—数学]