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(* 02110-1301 USA                                                     *)
(*****************************************************************************)
(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
(*****************************************************************************)
(*                                                                           *)
(*          Category Product                                                 *)
(*                                                                           *)
(*          Amokrane Saibi,  May 1994                                        *)
(*                                                                           *)
(*****************************************************************************)
Require Export Category.
Require Export SetoidPROD.
Set Implicit Arguments.
Unset Strict Implicit.
Section ProdCat.
Variable A B : Category.
Structure POb : Type :=  {Ob_l : A; Ob_r : B}.
Section pmor_setoid_def.
Variable u t : POb.
Structure Pmor : Type :=
{Hom_l : Ob_l u --> Ob_l t; Hom_r : Ob_r u --> Ob_r t}.
Definition Equal_Pmor (f g : Pmor) :=
Hom_l f =_S Hom_l g /\ Hom_r f =_S Hom_r g.

(* Specifications: *)
Lemma Equal_Pmor_equiv : Equivalence Equal_Pmor.
Canonical Structure Prod_Hom : Setoid := Equal_Pmor_equiv.