codensity monad


Let j:ACj\colon A \to C be a functor between categories. Its codensity monad is the right Kan extension Ran jjRan_j j of jj along itself, if this exists (as it certainly does when AA is small and CC is complete).

The name comes because jj is codense just when its codensity monad is the identity. Thus, in general, the codensity monad “measures the failure of jj to be codense”.

Last revised on September 22, 2012 at 18:11:59. See the history of this page for a list of all contributions to it.