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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	             Preservation of Limits               		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Limit.
Set Implicit Arguments.
Unset Strict Implicit.
(* Preservation de limites *)
(* F : J -> C *)
(* T : Delta(r) -> F *)
(* H : C -> D *)
(* T o H : Delta(r) -> F o H *)
Section comp_cone.
Variables (J C D : Category) (c : C) (F : Functor J C)
(T : Cone c F) (G : Functor C D).
Definition Comp_cone_tau (i : J) : G c --> (F o_F G) i := FMor G (T i).
(* revient a` prouver que : H(T(j)) = H(T(i)) o H(F g) *)

Lemma Comp_cone_tau_cone_law : Cone_law Comp_cone_tau.
Definition Comp_cone := Build_Cone Comp_cone_tau_cone_law.