Some categorical conditions are given that are sufficient to show that an enriched monad with a strength is a double exponential monad. The conditions hold for the double power locale monad (enriched over posets) and so as an application it is shown that the double power locale monad is a double exponential monad. A benefit is that this result about the double power locale monad can be established without the need for any detailed discussion of frame presentations or topos theory.
"When are enriched strong monads double exponential monads?." Bull. Belg. Math. Soc. Simon Stevin 23 (2) 311 - 319, may 2016. https://doi.org/10.36045/bbms/1464710120