(* definition de phi:C(F-,-) -> D(-,G-) *)
(* construction de phi *)
(* soit f: Fd ->c, phi(f)=ud o Gf : d -> G(Fd) *)
Section phi_ua_tau_def.
Variable dxc : POb (Dual D) C.
Definition PhiUA_arrow (f : UA_ob (UA_of (OB_l dxc)) --> Ob_r dxc) :=
UA_mor (UA_of (OB_l dxc)) o FMor G f.

(* Specifications: *)
Lemma PhiUA_arrow_map_law : Map_law PhiUA_arrow.
Canonical Structure PhiUA_tau := Build_Map PhiUA_arrow_map_law.