  We collect and systematize general definitions and facts on the application
of quantum groups to the construction of functional relations in the theory of
integrable systems. As an example, we reconsider the case of the quantum group
$U_q(\mathcal L(\mathfrak{sl}_2))$ related to the six-vertex model. We prove
the full set of the functional relations in the form independent of the
representation of the quantum group in the quantum space and specialize them to
the case of the six-vertex model.
