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?**