On the additivity of the little cubes operads

Abstract

We give a new proof of Dunn's additivity for the little $n$-cubes operads $C_n$, which has the advantage of being considerably shorter than the ones in the literature. At the end we remark on how our proof can be adjusted to work for the tensor product of a finite number of factors.

8 pages, 2 figures. We have added some extra remarks and improved the exposition; the proof of Lemma 5 has been fixed