14 Sep
2007
14 Sep
'07
8:50 a.m.
Greg Meredith asks,
... are there monads such that the only adjoint situations giving rise to them are the Kleisli and Eilenberg-Moore algebras?
NOt even the identity monad on SETS has this property, as it is the adjunction monad also for the adjoint pair [underlying pointset]: [topological spaces] --> SETS , [discrete topology on]: SETS --> [topological spaces] . There ARE a few monads for which the Kleisli and E-M categories "coincide," however, beyond the identity monads. First example coming to mind is the FreeVectorSpace monad on SETS. I'm sure other Categories-readers will point out more. -- Fred