ScalingStacks

Remark 1.5. The above notion of center provides a derived version of the Drinfeld center of a monoidal category (as defined in [JS]). To appreciate the difference, consider the abelian tensor category $R-\operatorname{mod}$ of modules over a (discrete) commutative ring $R$. Its classical Drinfeld center is $R-\operatorname{mod}$ again since there are no nontrivial $R$-linear braidings for $R$-modules. But as we will see below, the derived center of the $\infty$-category of $R$-modules is the $\infty$-category of modules over the Hochschild chain complex of $R$.