Toposes in algebraic quantum theory
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Tue, 04/05/2010 12:00 |
Chris Heunen (Comlab) |
Quantum Field Theory Seminar  |
L3 |
| Topology can be generalised in at least two directions: pointless topology, leading ultimately to topos theory, or noncommutative geometry. The former has the advantage that it also carries a logical structure; the latter captures quantum settings, of which the logic is not well understood generally. We discuss a construction making a generalised space in the latter sense into a generalised space in the former sense, i.e. making a noncommutative C*-algebra into a locale. This construction is interesting from a logical point of view, and leads to an adjunction for noncommutative C*-algebras that extends Gelfand duality. | |||