reserve B,C,D for Category;

theorem Th45:
  for S being Function of the carrier' of C,the carrier' of D holds /*(*'S) = S
proof
  let S be Function of the carrier' of C,the carrier' of D;
  now
    let f be Morphism of C;
    thus /*(*'S).f = (*'S).(f opp) by Def8
      .= S.(opp (f opp)) by Def10
      .= S.f;
  end;
  hence thesis by FUNCT_2:63;
end;
