There are many, many uses of the word "liberty," an issue I deal with at length in my book. Political libertarianism is an ideology demanding freedom from government coercion, which in practice they define as the state having legal authority over commerce and conduct. It is not equivalent to liberalism which understands that with liberty comes responsibility and that liberties are best formed by a constitutional rule of law.

Cooperation is not the same as governance. Non Randian libertarians are open to forms of cooperation but remain against the legal authority of governance and personal responsibility to the rule of law. "The state" is a straw man in the context of libertarianism.