  We define the sigma-model action for world-sheets with embedded defect
networks in the presence of a three-form field strength. We derive the defect
gluing condition for the sigma-model fields and their derivatives, and use it
to distinguish between conformal and topological defects. As an example, we
treat the WZW model with defects labelled by elements of the centre Z(G) of the
target Lie group G; comparing the holonomy for different defect networks gives
rise to a 3-cocycle on Z(G). Next, we describe the factorisation properties of
two-dimensional quantum field theories in the presence of defects and compare
the correlators for different defect networks in the quantum WZW model. This,
again, results in a 3-cocycle on Z(G). We observe that the cocycles obtained in
the classical and in the quantum computation are cohomologous.
