Functors which are determined, up to natural isomorphism, by their values on objects,  are called
 \emph{DVO} (\emph{Defined by Values on Objects}). 
 We focus on the collection of \emph{polynomial functors} on a category of sets (classes), 
 and we give a characterization theorem of the DVO functors over such collection of  functors.
 Moreover, we show that the ($\kappa$-bounded) powerset functor is \emph{not} DVO. 

Keywords: category of sets (classes), set functor, inclusion preserving functor, DVO functor.