Lambda the Ultimate

I have seen mentioned in this site that category theory is useful in clarifying the design process. I am wondering if the categorical approach would be any different from a purely functional approach. My reasoning is that in category theory, objects (states and data) are not important, if not almost entirely dismissable. What is of importance to the categorists is the relationships between objects, the functions, the way the structures work. It seems to beg the question, is category theory an abstraction of functional programming (not in an intuitive manner, but in the strict sense) and is there anythings that would be explanable in category theory that would not be in a functional language and the converse?