[[!redirects condensity monad]] It is not necessary for a functor to have an adjoint to canonically associate a monad to it. The *codensity monad of a functor $F$* (if it exists) is the right Kan extension of $F$ along itself. ## References * Tom Leinster, * where do monads come from?, post to the n-Café, [web](http://golem.ph.utexas.edu/category/2012/09/where_do_monads_come_from.html) * codensity and the ultrafilter monad, [arXiv:1209.3606 ](http://arxiv.org/abs/1209.3606)