reserve C for Category,
  C1,C2 for Subcategory of C;

theorem Th28:
  for C being Category, f being (Morphism of C),
  g being Element of (cod f) Hom holds g(*)f in (dom f) Hom
proof
  let C be Category, f be (Morphism of C), g be Element of (cod f) Hom;
  cod f = dom g by Th24;
  then dom (g(*)f) = dom f by CAT_1:17;
  hence thesis by Th24;
end;
