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If the Kleisli-category of a monad is Cartesian-closed, can we say when the category of Eilenberg-Moore algebras is?

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David, could you provide your motivations for this question? Personally, I find it easier to rummage up examples where the Eilenberg-Moore category of algebras (over a cartesian closed category) is cartesian closed, than I do for where the Kleisli category is cartesian closed. If you could provide examples of what you have in mind, that could be helpful. – Todd Trimble Aug 27 '10 at 19:18
If you're still interested in this, you might also be interested in this paper by Fiore and Menni: – Tom Leinster Dec 2 '11 at 18:01

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