  We study the general structure of 2-C*-categories closed under conjugation,
projections and direct sums. We do not assume units to be simple, i.e. for i_A
the 1-unit corresponding to an object A, the space Hom(i_A, i_A) is a
commutative unital C*-algebra. We show that 2-arrows can be viewed as
continuous sections in Hilbert bundles and describe the behaviour of the fibres
with respect to the categorical structure. We give an example of a
2-C*-Category giving rise to bundles of finite Hopf-algebras in duality. We
make some remarks concerning Frobenius algebras and Q-systems in the general
context of tensor C*-categories with non-simple units.
