字符串集合X上的代数结构

An algebraic structure in the set X~* of strings

本文利用相关函数的概念定义字符串集合 X~*上的一种范畴代数结构.讨论其上积特性,给出了左乘函子的定义,并证明了相关函数和两个左乘函子间的自然变换之对应关系.最后得出:X~*可等同于函子范畴(X~*→X~*)的一个子范畴.

This paper defines a categorical structure in the set X~* of strings using a concept of a related function.Its coproduct and left multiplicative functor are discussed,and the corre- spondence relationship between related functions and natural transformations of any two left multiplicative functors is described.Finally,it is found that X~* can be identified with the subcategory of the functor category(X~*→X~*).