Category theory for conformal boundary conditions

... inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius-Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity. We apply our results to the description of boundary conditions in twodimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives rise to a NIM-rep of the fusion rules, and discuss a possible relation with the representation theory of vertex operator algebras.