Sat 22 Sep 2012

## Unnatural Transformations and Quantifiers

Posted by Dan Doel under Category Theory , Haskell , Kan Extensions , Mathematics , Monads[3] Comments

Recently, a fellow in category land discovered a fact that we in Haskell land have actually known for a while (in addition to things most of us probably don't). Specifically, given two categories and , a functor , and provided some conditions in hold, there exists a monad , the codensity monad of .

In category theory, the codensity monad is given by the rather frightening expression: