 Functors on Set. The polynomial operators on sets extend to  endofunctors on Set.     The way that these operations are defined  on morphisms is straightforward and may be found in any book  on category theory.   Here is a brief summary:  For any set s, the constant functor with value s is a functor on Set.    It takes every function to  ids. For any two functors F and G, we have a functor  F× G defined by  (F× G)(a) = Fa × Ga; here we use the  cartesian product on sets.   If  f : a → b, then  