用图论方法判断范畴的特殊对象

Determining Special Objects of Category by Using Graph Theory Methods

用顶点表示范畴的对象,用有向边表示范畴的非恒等态射,则范畴可表示为一个没有环和重边的有向简单图.结合图论知识,构造了判断范畴的始对象、终对象和零对象的两个等价定理,并针对一些特殊范畴得出了相应的推论.

If we use vertices and directed edges to express objects and morphisms of category respective-ly,ignoring all identity morphisms, then a category can be expressed as a directed simple graph which has no rings or repeated edges. Combining the knowledge of graph theory, we establish two equivalent theorems which can be used to determine initial objects, terminal objects and zero objects of category. Moreover, we ob- tain some corresponding corollaries for some special categories.