Functor.Representable.Hom_Func.
NatTrans.Func_Cat NatTrans.NatIso.
Ext_Cons.Prod_Cat.Nat_Facts.
Local Open Scope functor_scope.
(** In this module we show uniqueness of local kan extensions by forming category of cones and showing that the local right kan extensions are terminal objects of those categories. *)
Section Facts.
Context {C C' : Category} (p : C –≻ C')
{D : Category} (F : C –≻ D).
Section LoKan_Cone_Morph_eq_simplify.
Context {Cn Cn' : LoKan_Cone p F} (M M' : LoKan_Cone_Morph Cn Cn').

(* Specifications: *)
(** Two local kan extension cone morphisms are equal if their underlying natural transformations are. *)
Theorem LoKan_Cone_Morph_eq_simplify : M = M' :> (_ –≻ _)%nattrans → M = M'.
End LoKan_Cone_Morph_eq_simplify.