Section comp_com_def.
Variables (axf bxg cxh : Com_ob) (f : Com_arrow axf bxg)
(g : Com_arrow bxg cxh).
Definition Comp_com_mor := Mor_com_arrow f o Mor_com_arrow g.
Canonical Structure Comp_com_arrow := Build_Com_arrow Comp_com_law.
End comp_com_def.
(* composition operator *)
Definition Comp_Comma := Build_Comp Comp_com_congl Comp_com_congr.
(* Id *)
Canonical Structure Id_Comma (axf : Com_ob) :=
Build_Com_arrow (Id_com_law axf).

Lemma Idl_Comma : Idl_law Comp_Comma Id_Comma.