Section fun_prod_map_def.
Variable c1 c2 : C.
Definition Fun_prod_mor (f : c1 --> c2) := Mor_prod C1 f (Id a).
Canonical Structure Fun_prod_map :
Map (c1 --> c2) (Fun_prod_ob c1 --> Fun_prod_ob c2) := Fun_prod_map_law.
End fun_prod_map_def.

Lemma Fun_prod_comp_law : Fcomp_law Fun_prod_map.