  Extending work of Saneblidze-Umble and others, we use diagonals for the
associahedron and multiplihedron to define tensor products of A-infinity
algebras, modules, algebra homomorphisms, and module morphisms, as well as to
define a bimodule analogue of twisted complexes (type DD structures, in the
language of bordered Heegaard Floer homology) and their one- and two-sided
tensor products. We then give analogous definitions for 1-parameter
deformations of A-infinity algebras; this involves another collection of
complexes. These constructions are relevant to bordered Heegaard Floer
homology.
