Let $k$ be an algebraically closed field of characteristic $0$. Let $R, S$ be two commutative $k$-algebras.

Let $\operatorname{Ch}(R), \operatorname{Ch}(S)$ be the categories of complexes of $R$-modules and $S$-modules, respectively.

**Question**
If $\operatorname{Ch}(R), \operatorname{Ch}(S)$ are equivalences as $k$-linear abelian categories, then $R \simeq S$ as $k$-algebras?

It is well-known that $\operatorname{Mod}(R) \simeq \operatorname{Mod}(S)$ implies $R \simeq S$, where $\operatorname{Mod}(R), \operatorname{Mod}(S)$ are the categories of $R$-modules and $S$-modules, respectively. This is a corollary of Morita equivalence. I consider a variation of this fact.

In the future, I want to consider a generalization in the case of commutative differential graded algebras.

Any comments and references are welcome. Thank you!

The same question is in MSE.