  The first imprimitivity theorems identified the representations of groups or
dynamical systems which are induced from representations of a subgroup.
Symmetric imprimitivity theorems identify pairs of crossed products by
different groups which are Morita equivalent, and hence have the same
representation theory. Here we consider commuting actions of groups $H$ and $K$
on a $C^*$-algebra which are saturated and proper as defined by Rieffel in
1990. Our main result says that the resulting Morita equivalence of crossed
products is natural in the sense that it is compatible with homomorphisms and
induction processes.
