Free products of higher operad algebras

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [Batanin-Weber, 2011], [Weber, 2011] and [Batanin-Cisinski-Weber, 2011] by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by a normalised n-operad in the sense of Batanin [Batanin, 1998], an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad.