Abstract: In order to define an A_\infty structure on the tensor product of two A_\infty algebras, one needs a diagonal map on the associahedra. Such a diagonal map has been constructed by Ron Umble and Samson Saneblidze, but their proofs are very technical and difficult to verify. We describe another approach being developed in collaboration with M. Markl that uses the cubical cell-complex for the associahedra arising in the Boardman-Vogt W-construction.