  Suppose a locally compact group G acts freely and properly on a locally
compact Hausdorff space X, and let gamma be the induced action on C_0(X). We
consider a category in which the objects are C*-dynamical systems (A, G, alpha)
for which there is an equivariant homomorphism of (C_0(X), gamma) into the
multiplier algebra M(A). Rieffel has shown that such systems are proper and
saturated, and hence have a generalized fixed-point algebra A^alpha which is
Morita equivalent to A times_{alpha,r} G. We show that the assignment (A,
alpha) maps to A^alpha is functorial, and that Rieffel's Morita equivalence is
natural in a suitable sense. We then use our results to prove a categorical
version of Landstad duality which characterizes crossed products by coactions,
and to prove that Mansfield imprimitivity for crossed products by homogeneous
spaces is natural.

Operator Algebras;Category Theory