  We present a study on the Yoneda-Dress construction of biset functors of
linear representations over a field of characteristic zero. We give a
characterization of their lattices of ideals and we provide a criterion of
vanishing for their essential algebras. We provide a parametrization for a
family of simple modules over the functor of rational representations. Finally,
we give an equivalence between the category of modules over the shifted functor
of complex class functions and the category of modules over a semisimple
algebra.
