Derived equivalences implying isomorphism of Hochschild cohomologies, question.

Question

Let $k$ be a field, let $A$ and $B$ be associative unital $k$-algebras, in this paper (http://webusers.imj-prg.fr/~bernhard.keller/publ/dih.pdf) Keller says that if there's an equivalence of derived categories

$\mathcal{D}(A) \xrightarrow{\sim}\mathcal{D}(B)$,

there's an isomorphism of graded algebras between their Hochschild cohomologies $HH(A,A)$ and $HH(B,B)$.

I wanted to ask:

Is $\mathcal{D}(A)$ the derived category of left $A$-modules, or the derived category of $A$-bimodules ??

Answer 1

He means the derived category of left (or right ... I forget whether he's left- or right-handed) modules. But if there's an equivalence of derived categories of left modules, then there's also an equivalence of derived categories of bimodules, which is the key to the result you quote.