  A modular fusion category C allows one to define projective representations
of the mapping class groups of closed surfaces of any genus. We show that if
all these representations are irreducible, then C has a unique Morita-class of
simple non-degenerate algebras, namely that of the tensor unit. This improves
on a result by Andersen and Fjelstad, albeit under stronger assumptions. One
motivation to look at this problem comes from questions in three-dimensional
quantum gravity.
