  In this article Hopf parametric adjunctions are defined and analysed within
the context of the 2-adjunction of the type $\mathbf{Adj}$-$\mathbf{Mnd}$. In
order to do so, the definition of adjoint objects in the 2-category of
adjunctions and in the 2-category of monads for $Cat$ are revised and
characterized. This article finalises with the application of the obtained
results on current categorical characterization of Hopf Monads.
