Duality for Convexity

Details Duality for Convexity Duality for Convexity

2009-11-19

arxiv.org/abs/0911.3834v1

Mathematics

Logic

Scientific paper

This paper studies convex sets categorically, namely as algebras of a distribution monad. It is shown that convex sets occur in two dual adjunctions, namely one with preframes via the Boolean truth values {0,1} as dualising object, and one with effect algebras via the (real) unit interval [0,1] as dualising object. These effect algebras are of interest in the foundations of quantum mechanics.

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