Let $HH_*(A,N)$ (or $HH^*(A,N)$) be the Hochschild homology (or cohomology) of an associative algebra $A$ with coefficients in an $A$-bimodule $N$.

I was reading nlab's entry on Hochschild cohomology and I saw this term:

Hochschild homology object of any bimodule over an monoid in a monoidal ($\infty ,1$)-category

, which, when $N = A$, is also called the ($\infty ,1$)- or derived center of $A$.

In this paper (http://arxiv.org/pdf/0805.0157v5.pdf) they say that for an associative algebra object $A$ in a closed symmetric monoidal $\infty$-category $\mathcal{S}$, the derived center or Hochschild cohomology $Z(A) = HH^*(A) \in \mathcal{S}$ is the endomorphism object $End_{A \otimes A^{op}} (A)$ of $A$ as an $A$-bimodule.

Then I found this on page 45:

6.2. Deligne-Kontsevich conjectures for derived centers.The notion of Drinfeld center for monoidal stable categories is a categorical analogue of Hochschild cohomology of associative (or $A_{\infty}$ algebras)...

Honestly I had never heard of Hochschild cohomology objects (or derived centers?) or Hochschild (co)homlogy used in this type of context but mostly I wanted to know:

**What is the relationship between Hochschild cohomology and Drinfeld centers?**