Section ylphi_tau_def.
Variables (a : C) (F : Functor C SET).
Definition YLphi_arrow (T : NT (FunSET a) F) := T a (Id a).
Canonical Structure YLphi_tau := Build_Map''0 YLphi_arrow_map_law.
End ylphi_tau_def.
(* de'montrer que YLphi_tau ve'rifie NT_law *)

Lemma YLphi_nt_law :
forall (a a' : C) (g : a --> a') (F F' : Functor C SET)
(T : NT F F') (U : NT (FunSET a) F),
YLphi_tau a' F' (NtH g o_NTv U o_NTv T) =_S
(FMor F g o T a') (YLphi_tau a F U).