CF Graphs Category and its Product and Upper Product

The concept of category came from the research of system science, which not only needed discuss the property of system itself but also the relationship between different systems. So we need to trade the system as an entirety and use the theory of category. Category is a basic concept of homological algebra and is created by Eilenberg and Maclane in 1945, has been applied to many fields of mathematics[1]. They use the language of category to depict elements of theirs and research its property. In this paper, we introduced category into graph and bring out a new concept of CF (classic and fuzzy)graph category based on the concept of homomorphism between two graphs which keeps the connexity of vertexes, and discussed its property of isomorphism and bring out the concept of product and upper product of it.