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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*	      A Functor which is a Right Adjoint is Continuous		     *)
(*                      (part of Freyd's Theorem)             		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Adj_UA.
Require Export Pres_Limits.
Set Implicit Arguments.
Unset Strict Implicit.
(* *)
Section ladj_pres.
Variables (C D : Category) (G : Functor C D) (la : LeftAdj G)
(J : Category) (H : Functor J C) (l : Limit H).
(* pour tout d : D et tau : Delta(d) -> T o G, sigma(i) = phi_1<d,Ti>(tau(i)) *)
Section lp_diese.
Variables (d : D) (tau : Cone d (H o_F G)).
Definition Lp_sigma_tau (i : J) := ApAphi_inv la (tau i:d --> G (H i)).
(* sigma est en fait un cone(T,Fd) ou` F est l'adjoint de G *)

Lemma Lp_sigma_tau_cone_law : Cone_law Lp_sigma_tau.
Definition Lp_sigma := Build_Cone Lp_sigma_tau_cone_law.