Integrals for braided Hopf algebras

Let H be a Hopf algebra in a rigid braided monoidal category with split idempotents. We prove the existence of integrals on (in) H characterized by the universal property, employing results about Hopf modules, and show that their common target (source) object IntH is invertible. The fully braided version of Radford's formula for the fourth power of the antipode is obtained. The relationship of integration with cross-product and transmutation is studied. The results apply to topological Hopf algebras which do not have an additive structure, e.g. a torus with a hole.