Deformations of monoidal functors

We point out that for Yetter's deformational Hochschild complex of a monoidal functor between abelian monoidal categories the Gerstenhaber-Voronov type operations can be defined making it a strong homotopy Gerstenhaber algebra. This encodes deformation theory of monoidal functors in an analogical way as deformation theory of associative algebras is described by the strong homotopy Gerstenhaber algebra structure on the corresponding Hochschild cochains. We describe a quasi-classical limit of deformations of a symmetric monoidal functor in terms of Poisson type structure.