
theorem Th6:
  for C being category, o1,o2 being Object of C st <^o1,o2^> <> {}
  & <^o2,o1^> <> {} for A being Morphism of o1,o2 holds A is iso iff A is
  retraction & A is coretraction
proof
  let C be category, o1,o2 be Object of C such that
A1: <^o1,o2^> <> {} & <^o2,o1^> <> {};
  let A be Morphism of o1,o2;
  thus A is iso implies A is retraction & A is coretraction by Th5;
  assume
A2: A is retraction & A is coretraction;
  then A" is_right_inverse_of A by A1,Def4;
  then
A3: A * A" = idm o2;
  A" is_left_inverse_of A by A1,A2,Def4;
  then A" * A = idm o1;
  hence thesis by A3;
end;
