 We regard  this system as a coalgebra (X, e), where  X = {x, y, z}, e(x) =  ⟨0,y⟩ ,   and similarly for e(y)  and z(x) . So now we have a concrete example  of a  coalgebra  for this F.   Another coalgebra for F uses the set N∞  of streams as its carrier set.   The coalgebra itself is   