Section prod_proj.
Variable A B : Category.
(* Fst *)
Canonical Structure Fst_map (a b : PROD A B) :=
Build_Map (Fst_map_law (a:=a) (b:=b)).
Canonical Structure Fst := Build_Functor Fst_comp_law Fst_id_law.
(* Snd *)

Lemma Snd_map_law : forall a b : PROD A B, Map_law (Hom_r (u:=a) (t:=b)).