  Imprimitivity theorems provide a fundamental tool for studying the
representation theory and structure of crossed-product C*-algebras. In this
work, we show that the Imprimitivity Theorem for induced algebras, Green's
Imprimitivity Theorem for actions of groups, and Mansfield's Imprimitivity
Theorem for coactions of groups can all be viewed as natural equivalences
between various crossed-product functors among certain equivariant categories.
  The categories involved have C*-algebras with actions or coactions (or both)
of a fixed locally compact group G as their objects, and equivariant
equivalence classes of right-Hilbert bimodules as their morphisms. Composition
is given by the balanced tensor product of bimodules.
  The functors involved arise from taking crossed products; restricting,
inflating, and decomposing actions and coactions; inducing actions; and various
combinations of these.
  Several applications of this categorical approach are also presented,
including some intriguing relationships between the Green and Mansfield
bimodules, and between restriction and induction of representations.
