Algèbre Pré-Gerstenhaber à homotopie près

Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding Koszul dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy: it is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts.