In the 1950s and 1960s there was a debate about the nature of an agricultural cooperative: the cooperative as extension of the farm, the cooperative as vertical integration or the cooperative as a firm. We revisit this debate with various concepts from the theory of the firm that have been formulated since 1990. Two concepts shed light on this debate: the enterprise as a system of attributes and the delineation of a governance structure in terms of ownership rights, control rights and income rights. We argue that viewing the cooperative as a system of attributes integrates these three views. It emphasizes that a cooperative is a firm in itself, with many independent input suppliers as owners. The feature of many input suppliers as owners implies that the behavioral differences between a cooperative and an investor owned firm have to be addressed by highlighting the unique aspects of the stakeholder owning the enterprise.