Section funy_map_def.
Variable a b : C.
Canonical Structure FunY_map := Build_Map0'' FunY_map_law.
End funy_map_def.
Canonical Structure FunY := Build_Functor0'' FunY_comp_law FunY_id_law.
(* lemma : Y is full *)

Lemma Y_full :
let f := fun (a b : C) (h : NT (FunSET a) (FunSET b)) => h a (Id a) in
Full_law0'' (F:=FunY) f.