We describe quantizations on monoidal categories of modules over finite groups. Those are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over $S_3$ and $A_4$ we give explicit forms for all quantizations.
"Quantizations of Group Actions." J. Gen. Lie Theory Appl. 6 1 - 15, 2012. https://doi.org/10.4303/jglta/G120403