On the additivity of the little cubes operads

TL;DR

This paper presents a concise new proof of Dunn's additivity theorem for little n-cubes operads, simplifying previous proofs and discussing extensions to multiple factors.

Contribution

A shorter, more streamlined proof of Dunn's additivity for little n-cubes operads, with potential for generalization to multiple tensor factors.

Findings

Proof of Dunn's additivity is significantly shorter.

Method can be adapted for tensor products of multiple factors.

Provides insights into the structure of little n-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.