My question is the following: is there an analog of Morita theorem in the simplicial setting?
I mean, we can define two simplicial rings $A,B$ to be simplicially Morita equivalent is the categories of simplicial modules $Mod(A)$ and $Mod(B)$ are equivalent (or maybe equivalent as simplicial categories?). Is there a result similar to the classical Morita theorem which gives a (simple) criterion for two rings to be Morita equivalent?
I tried to google, but I couldn't find anything useful. So I think maybe such an extension is just some trivial formality? Maybe it can easily be obtained from some well-known general result?
I have asked this question on math.stackexchenge, but didn't receive an answer (though comments there suggest that something like that should be true).
Thank you very much!