Abstract
Previous results about crossed modules over a braided Hopf algebra are applied to the study of quantum groups in braided categories. Cross products for braided Hopf algebras and quantum braided groups are constructed. Criteria for when a braided Hopf algebra or a quantum group is a cross product are obtained. A generalization of Majid's transmutation procedure for quantum braided groups is considered. A ribbon structure on a quantum braided group and its compatibility with cross product and transmutation are studied.
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