Scindements de foncteurs composés

A case of natural decomposition of plethysm is studied. We work within the category of functors between vector spaces over a prime field Fp. The symmetric power Sn○B of a functor B is shown to split when B takes p-boolean algebras values-these are algebras whose product satisfies xp=x. The injective envelope of the identity functor takes such values. This is applied to functor cohomology computations, which are relevant to the study of the cohomology of Eilenberg-Mac Lane spaces.