  This preprint contains a part of the results of our earlier preprint
arXiv:0907.3335v2 presented in a form suitable for journal publication.
  It covers a construction of a 2-fold monoidal structure on the category of
tetramodules, with all necessary definitions, and an overview of the results of
R.Taillefer [Tai1,2] on tetramodules and the Gerstenhaber-Schack cohomology
[GS] (formerly served as Appendix in arXiv:0907.3335v2), as well as a
computation of the Gerstenhaber-Schack cohomology for the free commutative
cocommutative bialgebra S(V), for a V is a vector space.
