Spahn codensity 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
  • codensity and the ultrafilter monad, arXiv:1209.3606