Section NatTrans_Props.
Context {C C' : Category}.
(** The identity natural transformation. The arrow family are just all identity arrows: *)
Program Definition NatTrans_id (F : (C –≻ C')%functor) : F –≻ F :=
{|
Trans := fun x : Obj => id
|}.

Theorem NatTrans_id_unit_left {F G : (C –≻ C')%functor} (N : F –≻ G)
: (NatTrans_id G) ∘ N = N.