  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.
