  The aim of this paper is to introduce an algebraic structure on the set of
all coalgebras with the same state space over the given type which allows us to
present definitions of weak and delay bisimulation for coalgebras.
Additionally, we introduce an algebraic structure on the carrier set of the
final coalgebra and characterize a special subcoalgebra of the final coalgebra
which is used in the formulation of the weak coinduction principle. Finally,
the new algebraic setting allows us to present a definition of an approximated
weak bisimulation, study its properties and compare it with previously defined
weak bisimulation for coalgebras.
