  For a non-vanishing group, we show that the evaluation functor induces an
equivalence between the category of modules over the double Burnside algebra
and a certain category of biset functors. Using this equivalence, we deduce
that over a field of characteristic zero, the double Burnside algebra of a
non-vanishing group is a quasi-hereditary algebra. We also show that the double
Burnside algebra over a field is self-injective if and only if it is
semisimple.
