End Prod_Functor_NatTrans_id.
Section Prod_Functor_NatTrans_compose.
Context {C D : Category}
{F G H : (C –≻ D)%functor}
(N1 : (F –≻ G)%nattrans)
(N2 : (G –≻ H)%nattrans)
{C' D' : Category}
{F' G' H' : (C' –≻ D')%functor}
(N1' : (F' –≻ G')%nattrans)
(N2' : (G' –≻ H')%nattrans).

Theorem Prod_Functor_NatTrans_compose :
((Prod_Functor_NatTrans N2 N2') ∘ (Prod_Functor_NatTrans N1 N1') =
Prod_Functor_NatTrans (N2 ∘ N1) (N2' ∘ N1'))%nattrans.