End comp_com_def.
(* composition operator *)

(* Specifications: *)
Lemma Comp_com_congl : Congl_law Comp_com_arrow.
Lemma Comp_com_congr : Congr_law Comp_com_arrow.
Definition Comp_Comma := Build_Comp Comp_com_congl Comp_com_congr.
Lemma Assoc_Comma : Assoc_law Comp_Comma.
(* Id *)
Lemma Id_com_law : forall axf : Com_ob, Com_law (Id (Ob_com_ob axf)).
Canonical Structure Id_Comma (axf : Com_ob) :=
Build_Com_arrow (Id_com_law axf).
Lemma Idl_Comma : Idl_law Comp_Comma Id_Comma.
Lemma Idr_Comma : Idr_law Comp_Comma Id_Comma.
Canonical Structure Comma := Build_Category Assoc_Comma Idl_Comma Idr_Comma.