reserve x,y for set;

theorem Th5:
  for A,B being category, F being Functor of A,B st F is bijective
  for G being Functor of B,A st G*F = id A holds the FunctorStr of G = F"
proof
  let A,B be category, F be Functor of A,B;
  assume
A1: F is bijective;
  then reconsider FF = F" as feasible FunctorStr over B,A by FUNCTOR0:35;
A2: F*FF = id B by A1,FUNCTOR1:18;
  let G be Functor of B,A;
  assume G * F = id A;
  then (id A)*FF = G * id B by A2,FUNCTOR0:32
    .= the FunctorStr of G by FUNCTOR3:5;
  hence thesis by FUNCTOR3:4;
end;
