  We study properties of the category of modules of an algebra object A in a
tensor category C. We show that the module category 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
two-dimensional 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.
