Finite sets and symmetric simplicial sets.
On décrit les foncteurs polynomiaux, des groupes abéliens libres vers les groupes abéliens, comme des diagrammes de groupes abéliens dont on explicite les relations.
The purpose of this paper is two fold: we study the behaviour of the forgetful functor from -modules to graded vector spaces in the context of algebras over an operad and derive the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for those Hopf algebras.Let denote the forgetful functor from -modules to graded vector spaces. Left modules over an operad are treated as -algebras in the category of -modules. We generalize the results obtained...