  Using factorization homology techniques, we give a simple proof of the action
of Kontsevich and Soibelman operad on the pair consisting of Hochschild
cohomology and Hochschild homology. The proof obviously extends to higher
Hochschild cohomology and factorization (also called chiral) homology. Note
that our result works in categories of chain complexes but also in categories
of modules over a commutative ring spectrum.
