  We describe types of double magma associated with Ward quasigroups, double
Ward quasigroups, their duals and the groups they generate. Ward quasigroup
double magma and unipotent, right modular, left unital double magma are proved
to be improper. Necessary and sufficient conditions are found on a pair of
right modular, left unital magma (and right-left unital magma) for them to form
a double magma. We give further insight into the intimate connection between
mediality and the interchange law by proving that a quasigroup is medial if and
only if any pair of its parastrophic binary operations satisfy the interchange
law.
