Homotopy Gerstenhaber structure on deformation complex of a morphism

Ginfinity -structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a Binfinity -algebra by an associative algebra. Actions of Binfinity -algebras on associative and Binfinity -algebras are analyzed, extensions of Binfinity -algebras by associative and Binfinity -algebras, that they act upon, are constructed. The resulting Ginfinity -algebra on the deformation complex of a morphism is shown to be quasi-isomorphic to the Ginfinity -algebra on deformation complex of the corresponding diagram algebra. Linfinity -structure is described on the Hochschild complex of a morphism.