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

theorem Th27:
  for C being Category, f being (Morphism of C), g being Element of Hom dom f
  holds f(*)g in Hom cod f
proof
  let C be Category, f be (Morphism of C), g be Element of Hom dom f;
  cod g = dom f by Th23;
  then cod (f(*)g) = cod f by CAT_1:17;
  hence thesis by Th23;
end;
