Partially ordered monads for topology, Kleene algebra and rough sets

In this talk we will show that partially ordered monads contain sufficient structure for modelling rough sets, Kleene algebras and monadic topologies. Rough sets are modelled in a generalized setting with set functors. Further, we show how partially ordered monads can be used in order to obtain a generalised notion of Kleene powerset algebras building upon more general powerset functor settings beyond strings and relations. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification theory can be developed.