(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(*****************************************************************************)
(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
(*****************************************************************************)
(*                                                                           *)
(*          Category Theory : Hom Functors                                   *)
(*                                                                           *)
(*          Amokrane Saibi May 1994                                          *)
(*                                                                           *)
(*****************************************************************************)
Require Export SET.
Require Export Functor.
Require Export Dual.
Set Implicit Arguments.
Unset Strict Implicit.
(* 1. Hom-Functor : C(a,-) : C-->SET *)
Section funset.
Variables (C : Category) (a : C).
(* to each object b of C, we associate Hom(a,b), a object of SET *)
Definition FunSET_ob (b : C) := a --> b.
Section funset_map_def.
Variable b c : C.
Section funset_mor_def.
Variable f : b --> c.
Definition FunSET_mor1 (g : a --> b) := g o f.

(* Specifications: *)
Lemma FunSET_map_law1 : Map_law FunSET_mor1.
Canonical Structure FunSET_mor : Map (FunSET_ob b) (FunSET_ob c) :=
FunSET_map_law1.