theorem Th42:
  for F being Functor of A,B, G being Functor of B,A for I being
  Functor of A,A st I ~= id A holds F*I ~= F & I*G ~= G
proof
  let F be Functor of A,B, G be Functor of B,A;
  let I be Functor of A,A;
  F*id A = F & id A*G = G by FUNCT_2:17;
  hence thesis by Th41;
end;
