Section comp_mon.
Variables (m1 m2 m3 : Monoid) (f : MonMor m1 m2) (g : MonMor m2 m3).
Definition Comp_MonMor_map := f o_M g.
Canonical Structure Comp_MonMor : MonMor_setoid m1 m3 :=
Build_MonMor Comp_MonMor_unit_law Comp_MonMor_op_law.
End comp_mon.
Definition Comp_MON := Build_Comp Comp_MonMor_congl Comp_MonMor_congr.

Lemma Assoc_MON : Assoc_law Comp_MON.