**21 October 2008**-
2:30 - 4:00 Gavin Seal

Order-adjoint monads

An order-adjoint monad is essentially a monad on SET whose functor allows for order-adjoint situations in its codomain. Given such a monad T, one can construct the category Kleisli monoids (that is, of monoids in the hom-sets of the associated Kleisli category), over which the category of T-algebras is monadic. The T-algebras can alternatively be characterized as certain injective objects in the category of Kleisli monoids. In this talk, we will go over the OctoberFest talk in more details, and relate those results with injective objects.