In the $\infty$-world, connective spectra play the role of abelian groups, while $\mathbb{E}_\infty$-spaces play that of commutative monoids. This may be rephrased by saying that we may identify the $\infty$-categories of spectra and $\mathbb{E}_\infty$-spaces with the $\infty$-categories $\mathsf{Mon}_{\mathbb{E}_\infty}(\mathcal{S})$ and $\mathsf{Grp}_{\mathbb{E}_{\infty}}(\mathcal{S})$ of $\mathbb{E}_\infty$-monoids/groups in the $\infty$-category of anima $\mathcal{S}$.

Now, the $1$-categories $\mathsf{Ab}$ and $\mathsf{CMon}$ come equipped with tensor products $\otimes_{\mathbb{Z}}$ and $\otimes_{\mathbb{N}}$. These correspond in homotopy theory to the tensor products of connective spectra and $\mathbb{E}_\infty$-spaces.

While the tensor product of connective spectra is widely discussed in the literature, I'm finding it a bit difficult to find references for that of $\mathbb{E}_\infty$-spaces. (So far I've only found discussion of this in arXiv:1305.4550).

Questions:

• What are some other references discussing the tensor product of $\mathbb{E}_\infty$-spaces?
• What is the unit of this tensor product?
• Finally, what are some concrete examples of it?