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

Hopf Parametric Adjoint Objects through a 2-adjunction of the type Adj-Mnd