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Stream: learning: questions

Topic: adjunction from known monad and comonad?

view this post on Zulip Asad Saeeduddin (Jan 26 2022 at 02:21):

Given a pair of functors F : A -> B and G : B -> A, if GF is a monad, and FG is a comonad, is there a canonical adjunction F -| G?

view this post on Zulip Asad Saeeduddin (Jan 26 2022 at 03:53):

@Callan McGill showed a counterexample: an equivalence FG is not necessarily adjoint, yet yields both a monad and a comonad