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Functional representations of monads in duality theory
Description:  It is well known that Stone's classical duality theorems can be generalised to categories of spaces and continuous relations. For example, Halmos's duality theorem affirms that the category of Stone spaces and Boolean relations (relations which are continuous in an appropriate sense) is dually equivalent to the category of Boolean algebras with "hemimorphisms", that is, maps preserving finite suprema but not necessarily finite infima. Recently, we showed how to use a functional representation of a monad to deduce this type of duality results in a generic and uniform manner. In this talk we present a functional representation of the Vietoris monad in the category of ordered compact Hausdorff spaces. Furthermore, we explain how this representation can lead to duality theorems for ordered compact Hausdorff spaces which can be interpreted as metric versions of Stone's classical results.
Joint work with Dirk Hofmann.
Date:  2015-10-13
Start Time:   15:30
Speaker:  Pedro Nora (Univ. Aveiro)
Institution:  Univ. Aveiro
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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