Weak Frobenius monads and Frobenius bimodules

Original · EN

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).