Short version, 2Sep

- Corrected typos.

- Inserted note after definition of morphism of partial algebras and
 of partial tensor categories saying that necessarily \phi(k) \cap \phi(l) is
 empty for k not equal to l so that \phi corresponds to an I-labeled
 partition of J

- In Theorem 2.14 and Corollary 2.15, removed the assumption that the
  partial Hopf algebra is regular. The fact that the left bidual of X
  isomorphic to X uses only the fact that both are a left and a right
  dual of the dual of X, respectively, and semi-simplicity. Also,
 added a reference for this fact.

- Slightly shortened the proof of Proposition 2.19, making more direct
  use of Peter-Weyl.

- Before of Theorem 3.13, explained what we mean by a partial compact
  quantum group being based over a partition phi.