ScalingStacks

Definition 5.11. For an $\mathcal{E}_{\infty}$-algebra $A$, we define the $\mathcal{E}_{n}$-Hochschild homology

$$\hh_{*}^{\mathcal{E}_{n}}(A)=A\otimes_{U_{A}}A$$

to be the tensor product of $A$ with itself over the algebra $U_{A}$.