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 *)
Canonical Structure Snd_map (a b : PROD A B) :=
Build_Map (Snd_map_law (a:=a) (b:=b)).

Lemma Snd_id_law : Fid_law Snd_map.