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(* 02110-1301 USA                                                     *)
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(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
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(*                                                                           *)
(*          Category Theory : Dual Category                                  *)
(*                                                                           *)
(*          Amokrane Saibi May 1994                                          *)
(*                                                                           *)
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Require Export Category.
Set Implicit Arguments.
Unset Strict Implicit.
Section d_cat.
Variable C : Category.
Definition DHom (a b : C) := b --> a.
(* construire un Comp_Type *)
Definition Comp_Darrow (a b c : C) (df : DHom a b) (dg : DHom b c) := dg o df.

(* Specifications: *)
Lemma Comp_dual_congl : Congl_law Comp_Darrow.
Lemma Comp_dual_congr : Congr_law Comp_Darrow.
Definition Comp_Dual := Build_Comp Comp_dual_congl Comp_dual_congr.
Lemma Assoc_Dual : Assoc_law Comp_Dual.
Lemma Idl_Dual : Idl_law (Hom:=DHom) Comp_Dual (Id (c:=C)).
Lemma Idr_Dual : Idr_law (Hom:=DHom) Comp_Dual (Id (c:=C)).
Canonical Structure Dual := Build_Category Assoc_Dual Idl_Dual Idr_Dual.