MONADS AND ALGEBRAS We have, from various sources, found the following examples of algebras related to monads: - The Kleisli category over the usual powerset monad is isomorphic to the category of sets and relations. - The Eilenberg-Moore category of the usual powerset monad is isomorphic to the category of complete lattices and join-preserving maps. - The Kleisli category of the term monad coincides with its Eilenberg-Moore category and is isomorphic to the category of $\Omega$-algebras. (Is this really true?) - The Eilenberg-Moore category over the (covariant?) double powerset monad is isomorphic to the category of complete atomic Boolean algebras. (What about the contravariant double?) - The Eilenberg-Moore category over the filter monad is isomorphic to the category of continuous lattices. - The Eilenberg-Moore category over the ultrafilter monad is isomorphic to compact Hausdorff spaces. Are there further well- or worse-known examples? Are there survey papers on this, also including proofs? Best regards, Patrik Eklund Umea University, Sweden