Studying two-dimensional field theories in the presence of defect lines naturally gives rise tomonoidal categories: their objects are the different ( topological) defect conditions, their morphisms are junction fields, and their tensor product describes the fusion of defects. These categories should be equipped with a duality operation corresponding to reversing the orientation of the defect line, providing a rigid and pivotal structure. We make this structure explicit in topological Landau-Ginzburg models with potential x(d), where defects are described by matrix factorisations of x(d) - y(d). The duality allows to compute an action of defects on bulk fields, which we compare to the corresponding N = 2 conformal field theories. We find that the two actions differ by phases.