  We consider traces on module categories over pivotal fusion categories which
are compatible with the module structure. It is shown that such module traces
characterise the Morita classes of special haploid symmetric Frobenius
algebras. Moreover, they are unique up to a scale factor and they equip the
dual category with a pivotal structure. This implies that for each pivotal
structure on a fusion category over the complex numbers there exists a
conjugate pivotal structure defined by the canonical module trace.
