RCFT with defects: Factorization and fundamental world sheets

It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditions, and that there is a small set of fundamental correlators to which all others are related via factorization - provided that the world sheets considered do not contain any non-trivial defect lines. In this paper we generalize both results to oriented world sheets with an arbitrary network of topological defect lines.