  Much of algebra and representation theory can be formulated in the general
framework of tensor categories. The aim of this paper is to further develop
this theory for braided tensor categories. Several results are established that
do not have a substantial counterpart for symmetric tensor categories. In
particular, we exhibit various equivalences involving categories of modules
over algebras in ribbon categories. Finally we establish a correspondence of
ribbon categories that can be applied to, and is in fact motivated by, the
coset construction in conformal quantum field theory.
