  A detailed construction of the universal integrability objects related to the
integrable systems associated with the quantum group $\mathrm U_q(\mathcal
L(\mathfrak{sl}_2))$ is given. The full proof of the functional relations in
the form independent of the representation of the quantum group on the quantum
space is presented. The case of the general gradation and general twisting is
treated. The specialization of the universal functional relations to the case
when the quantum space is the state space of a discrete spin chain is
described. This is a degression of the corresponding consideration for the case
of the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_3))$ with an
extensions to the higher spin case.
