We continue our earlier investigation on generalized reproducing kernels, in
connection with the complex geometry of $C^*$- algebra representations, by
looking at them as the objects of an appropriate category. Thus the
correspondence between reproducing $(-*)$-kernels and the associated Hilbert
spaces of sections of vector bundles is made into a functor. We construct
reproducing $(-*)$-kernels with universality properties with respect to the
operation of pull-back.

We survey some aspects of the pseudo-differential Weyl calculus for
irreducible unitary representations of nilpotent Lie groups, ranging from the
classical ideas to recently obtained results. The classical Weyl-H\"ormander
calculus is recovered for the Schr\"odinger representation of the Heisenberg
group. Our discussion concerns various extensions of this classical situation
to arbitrary nilpotent Lie groups and to some infinite-dimensional Lie groups
that allow us to handle the magnetic pseudo-differential calculus.