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

Abstract: 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.