Bimonadic adjunctions and the Explicit Basis property
M. Menni · 2009
Call an adjunction L a R : X ! Y bimonadic if R is monadic and L comonadic. (For example, for many monads on the category of sets, the induced Eilenberg-Moore adjunction is bimonadic [1, 2]. Also, many of the examples in [3] suggest that it is not uncommon for monads satisfying the Explicit Basis (EB) property to induce bimonadic Eilenberg-Moore adjunctions.) For such an adjunction, denote by M the induced monad on Y and by C the induced comonad on X . Following a suggestion by F. W. Lawvere we characterize the comonads C such that M satises the EB property.