Section Prod_Functor_compose.
Context {C D E: Category} (F : C –≻ D) (G : D –≻ E)
{C' D' E': Category} (F' : C' –≻ D') (G' : D' –≻ E').

Theorem Prod_Functor_compose :
((Prod_Functor G G') ∘ (Prod_Functor F F') =
Prod_Functor (G ∘ F) (G' ∘ F'))%functor.