Categorical landstad duality for actions

We show that the category JA(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate*-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C*(G),5c); and also that JA(G) is equivalent, via a reduced- crossed-product functor, to a comma category of normal coactions under the comultiplication. This extends classical Landstad duality to a category equivalence, and allows us to identify those C*-algebras which are isomorphic to crossed products by G as precisely those which form part of an object in the appropriate comma category.