Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category 𝓒 with a distinguished object, a symmetric special Frobenius algebra A in 𝓒, via the so-called TFT-construction. These correlators satisfy in particular all factorization constraints, which involve gluing homomorphisms relating correlators of world sheets of different topology.
We review the action of the gluing homomorphisms and discuss the implications of the factorization constraints for boundary conditions. The so-called classifying algebra 𝓐 for a RCFT is a semisimple commutative associative complex algebra, which classifies the boundary conditions of the theory. We show that the annulus partition functions can be obtained from the representation theory of 𝓐.