reserve C for category,
  o1, o2, o3 for Object of C;

theorem
  for C being non empty AltCatStr, O, A being Object of C for M being
  Morphism of A, O st O is initial holds M is epi
proof
  let C be non empty AltCatStr, O, A be Object of C, M be Morphism of A, O
  such that
A1: O is initial;
  let o be Object of C such that
A2: <^O,o^> <> {};
  let a, b be Morphism of O, o such that
  a * M = b * M;
  consider N being Morphism of O, o such that
  N in <^O,o^> and
A3: for M1 being Morphism of O, o st M1 in <^O,o^> holds N = M1 by A1,
ALTCAT_3:25;
  thus a = N by A2,A3
    .= b by A2,A3;
end;
