reserve A,B,C,D for Category,
  F for Functor of A,B,
  G for Functor of B,C;
reserve o,m for set;

theorem
  A ~= B & B ~= C implies A ~= C
proof
  given F1 being Functor of A,B such that
A1: F1 is isomorphic;
  given F2 being Functor of B,C such that
A2: F2 is isomorphic;
  take F2*F1;
  thus thesis by A1,A2,Th12;
end;
