Section const_map_def.
Variable a1 a2 : A.
Definition Const_mor (f : a1 --> a2) := Id b.
Canonical Structure Const_map :
Map (a1 --> a2) (Const_ob a1 --> Const_ob a1) := Const_mor_map_law.
End const_map_def.

Lemma Const_comp_law : Fcomp_law Const_map.