As shown by S. Eilenberg and J.C. Moore (1965), for a monad F with right
adjoint comonad G on any catgeory A, the category of unital
F-modules AF is isomorphic to the category of counital
G-comodules AG. The monad F is Frobenius provided we have F=G
and then AF≃AF. Here we investigate which kind of
equivalences can be obtained for non-unital monads (and non-counital comonads).Comment: 21 pages, the material is rearranged and the presentation is improve