Section diag_map_def.
Variable a b : C.
Definition Diag_mor (f : a --> b) :=
Build_Pmor (u:=Diag_ob a) (t:=Diag_ob b) f f.
Canonical Structure Diag_map := Build_Map Diag_map_law.
End diag_map_def.

Lemma Diag_comp_law : Fcomp_law Diag_map.