@Matthew,

> This restricts us from looking at one of the cutest adjunction constructions I know. If we have a Monad m, we compute two adjunctions! It's a classic construction. I don't think it's in Fong and Spivak **It is at the heart of the >=> operator in Haskell** if you've ever used it.
> However, I think I know why Kmett came up his adjunctions library the way he did. He has another adjunction construction he came up with 10 years ago. But his is all in Category (->).
> I can talk about these if you like.

You've piqued my curiosity.