Reading Scholze's notes on Condensed Mathematics it is mentioned that when considered as $\infty$-categories,


$$ D(\operatorname{Cond(Ab)}) \cong \operatorname{Cond}(D(\operatorname{Ab}))$$


and that this is not a feature of condensed abelian groups but rather of the category of sheaves on a site.


I have been looking for references on this fact, but haven't been able to find anything. [This thread](https://mathoverflow.net/questions/265557/sheaves-of-complexes-and-complexes-of-sheaves/265625) seems to suggest that we have some additional conditions on our site. Any references to read further on this and see why this is true for this example would be greatly appreciated.



Derived category of abelian sheaves on a site equivalent to sheaves on the derived category of abelian groups
It's true in any $1$-topos for hypercomplete sheaves, see Theorem 2.1.2.2 in [Spectral Algebraic Geometry](https://www.math.ias.edu/%7Elurie/papers/SAG-rootfile.pdf).


