  Two-dimensional conformal field theory (CFT) can be defined through its
correlation functions. These must satisfy certain consistency conditions which
arise from the cutting of world sheets along circles or intervals. The
construction of a (rational) CFT can be divided into two steps, of which one is
complex-analytic and one purely algebraic. We realise the algebraic part of the
construction with the help of three-dimensional topological field theory and
show that any symmetric special Frobenius algebra in the appropriate braided
monoidal category gives rise to a solution. A special class of examples is
provided by two-dimensional topological field theories, for which the relevant
monoidal category is the category of vector spaces.
