ption of the algebraic structure obtained this way, and a complete proof that this leads to a Gerstenhaber algebra is then obtained from an operadic approach.
This, in particular, considerably generalises the classical construction given by Gerstenhaber himself.
Conjecturally, the algebraic structure we describe should produce a Gerstenhaber algebra for an arbitrary monoidal category enriched over abelian groups, but even the bilinearity of the cup product and of the Lie-type bracket defined by the abstract