  The paper presents a detailed description of duality for braided algebras,
coalgebras, bialgebras, Hopf algebras and their modules and comodules in the
infinite setting. Assuming that the dual objects exist, it is shown how a given
braiding induces compatible braidings for the dual objects, and how actions
(resp. coactions) can be turned into coactions (resp. actions) of the dual
coalgebra (resp. algebra), with an emphasis on braided bialgebras and their
braided (co)module algebras.
