Leibniz rules and reality conditions

An analysis is made of reality conditions within the context of non-commuta tive geometry. We show that if a covariant derivative satisfies a given lef t Leibniz rule then a right Leibniz rule fixes the reality condition for th e covariant derivative itself. We show also that the map which determines t he right Leibniz rule must satisfy the braid equation if the extension of t he covariant derivative to tensor products is to satisfy the reality condit ion.