Recently I stumbled on the following: I find it hard to believe that they are not well-known facts. I would be grateful for references ... (a) The conditions for the Kleisli category of a monoidal monad to be closed (left/right) w.r.t the induced tensor when the original category is (left/right) closed. (b) The fact that, in the above situation, when the monad is idempotent the Kleisli category is always closed. With thanks in advance -robin (Robin Cockett)