Tensor products of A-infinty algebras with higher homotopy inner products (joint work with T. Tradler) The combinatorial structure of T. Tradler´s A-infinity algebras with higher homotopy inner products is controlled by a family of contractible polytopes called pairahedra. In this talk we construct an explicit combinatorial diagonal on the pairahedra and use it to define a tensor product of A-infinity algebras with higher homotopy inner products. In particular, cyclic A-infinity algebras are A-infinity algebras with trivial higher homotopy inner products. Thus the tensor product of cyclic A-infinity algebras is an A-infinity algebra with (typically non-trivial) higher homotopy inner products.