  We adapt a construction due to Troesch to the category of strict polynomial
superfunctors in order to construct complexes of injective objects whose
cohomology is isomorphic to Frobenius twists of the (super)symmetric power
functors. We apply these complexes to construct injective resolutions of the
even and odd Frobenius twist functors, to investigate the structure of the
Yoneda algebra of the Frobenius twist functor, and to compute other extension
groups between strict polynomial superfunctors.
