reserve
  I for set,
  E for non empty set;

theorem
  for C being category, A being ObjectsFamily of {},C
  for B being Object of C st B is initial holds
  B is A-CatCoproduct-like
  proof
    let C be category;
    let A be ObjectsFamily of {},C;
    let B be Object of C;
    assume B is initial;
    then ex P being MorphismsFamily of A,B st
    P is empty coprojection-morphisms by Th2;
    hence thesis;
  end;
