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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 : Natural Transformations between Hom-Functors           *)
(*                                                                           *)
(*          Amokrane Saibi May 1994                                          *)
(*                                                                           *)
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Require Export HomFunctor.
Require Export Ntransformation.
Set Implicit Arguments.
Unset Strict Implicit.
(* Natural transformation Y(f):C(b,-)-->C(a,-), with f:a-->b in C *)
Section funset_nt.
Variables (C : Category) (b a : C) (f : a --> b).
Section nth_map_def.
Variable c : C.
Definition NtH_arrow (h : b --> c) := f o h.

(* Specifications: *)
Lemma NtH_map_law : Map_law NtH_arrow.
Definition NtH_map : Map (FunSET b c) (FunSET a c) := NtH_map_law.