  Algebra and representation theory in modular tensor categories can be
combined with tools from topological field theory to obtain a deeper
understanding of rational conformal field theories in two dimensions: It allows
us to establish the existence of sets of consistent correlation functions, to
demonstrate some of their properties in a model-independent manner, and to
derive explicit expressions for OPE coefficients and coefficients of partition
functions in terms of invariants of links in three-manifolds.
  We show that a Morita class of (symmetric special) Frobenius algebras $A$ in
a modular tensor category $\calc$ encodes all data needed to describe the
correlators. A Morita-invariant formulation is provided by module categories
over $\calc$. Together with a bimodule-valued fiber functor, the system (tensor
category + module category) can be described by a weak Hopf algebra.
  The Picard group of the category $\calc$ can be used to construct examples of
symmetric special Frobenius algebras. The Picard group of the category of
$A$-bimodules describes the internal symmetries of the theory and allows one to
identify generalized Kramers-Wannier dualities.
