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 Th5:
  F is isomorphic implies for g being Morphism of B ex f being
  Morphism of A st F.f = g
proof
  assume
A1: F is isomorphic;
  let g be Morphism of B;
  rng F = the carrier' of B by A1;
  then consider f being object such that
A2: f in dom F and
A3: F.f = g by FUNCT_1:def 3;
  reconsider f as Morphism of A by A2;
  take f;
  thus thesis by A3;
end;
