(** Given a cone, we construct a cone morph to the cone morph that we constructed above. *)
Program Definition Cone_Morph_to_Cone_for_LoKan :
LoKan_Cone_Morph Cn Cone_for_LoKan :=
{|
cone_morph :=
(((rke _a (cone_edge Cn))%morphism)
∘ (Trans (adj_unit (right_kan_ext_adj rke)) Cn))%nattrans
|}.
Next Obligation.
End Cone_Morph_to_Cone_for_LoKan.
Section Cone_Morph_to_Cone_for_LoKan_Unique.
Context {Cn : LoKan_Cone p F} (M M' : LoKan_Cone_Morph Cn Cone_for_LoKan).

(** Cone morph to the cone constructed is unique. *)
Theorem Cone_Morph_to_Cone_for_LoKan_Unique : (M = M' :> (_ –≻ _)%nattrans).
End Cone_Morph_to_Cone_for_LoKan_Unique.