Editing Monad (category theory) (section)

===Codensity monads===

Under mild conditions, functors not admitting a left adjoint also give rise to a monad, the so-called [[codensity monad]]. For example, the inclusion

:<math>\mathbf{FinSet} \subset \mathbf{Set}</math>

does not admit a left adjoint. Its codensity monad is the monad on sets sending any set ''X'' to the set of [[ultrafilter]]s on ''X''. This and similar examples are discussed in {{harvtxt|Leinster|2013}}.