Entrepreneurship is not a synonym for management science. Asking if it is equivalent or a member of the set of "management sciences" does not "beg the question

Entrepreneurship is not a synonym for management science. Asking if it is equivalent or a member of the set of "management sciences" does not "beg the question." If by "the validity of category Y is not established" you mean that the validity of management science is not established I think you are ignoring a body of work dating to the 1940's in applying mathematics to decision making. Disciplines like industrial engineering or operations research are normally considered members of the set of management science. They substitute decision making based on models and simulation for naive methods based on intuition and rules of thumb. Examples would include inventory control theory, queueing theory, game theory, decision analysis,... See for example http://en.wikipedia.org/wiki/Management_science http://en.wikipedia.org/wiki/Management_science and http://en.wikipedia.org/wiki/Operations_research http://en.wikipedia.org/wiki/Operations_research