theorem
  for f being Morphism of a,b st a is initial holds init(a,b) = f
proof
  let f be Morphism of a,b;
  assume
A1: a is initial;
  then Hom(a,b) <> {};
  then dom f = a & cod f = b by CAT_1:5;
  hence thesis by A1,Th39;
end;
