  An analysis is made of reality conditions within the context of
noncommutative geometry. We show that if a covariant derivative satisfies a
given left Leibniz rule then a right Leibniz rule is equivalent to the reality
condition. We show also that the matrix which determines the reality condition
must satisfy the Yang-Baxter condition if the extension of the covariant
derivative to tensor products is to satisfy the reality condition. This is
equivalent to the braid condition for the matrix which determines the right
Leibniz rule.
