  We give explicit combinatorial descriptions of three Schur functors arising
in the theory of pre-Lie algebras. The first of them leads to a functorial
description of the underlying vector space of the universal enveloping pre-Lie
algebra of a given Lie algebra, strengthening the PBW theorem of Segal. The two
other Schur functors provide functorial descriptions of the underlying vector
spaces of the universal multiplicative enveloping algebra and of the module of
K\"ahler differentials of a given pre-Lie algebra. An important consequence of
such descriptions is an interpretation of the cohomology of a pre-Lie algebra
with coefficients in a module as a derived functor for the category of modules
over the universal multiplicative enveloping algebra.
