Section Prod_Functor_NatTrans_id.
Context {C D : Category} (F : (C –≻ D)%functor)
{C' D' : Category} {F' : (C' –≻ D')%functor}.

Theorem Prod_Functor_NatTrans_id :
Prod_Functor_NatTrans (NatTrans_id F) (NatTrans_id F') =
NatTrans_id (Prod_Functor F F').