End Hor_Compose_ids.
(** Horizontal composition of opposite of two natural transformations is just the opposite of the horizontal composition of those two natural transformations. *)
Section Hor_Compose_NOP.
Context {C D E : Category} {F G : (C –≻ D)%functor} {F' G' : (D –≻ E)%functor}
(N : F –≻ G) (N' : F' –≻ G').

Theorem NatTrans_hor_comp_Op : ((N' ∘_h N)^op = N'^op ∘_h N^op)%nattrans.
End Hor_Compose_NOP.