  We discuss algebraic and representation theoretic structures in braided
tensor categories C which obey certain finiteness conditions. Much interesting
structure of such a category is encoded in a Hopf algebra H in C. In
particular, the Hopf algebra H gives rise to representations of the modular
group SL(2,Z) on various morphism spaces. We also explain how every symmetric
special Frobenius algebra in a semisimple modular category provides additional
structure related to these representations.
