Duality for Convexity

Bart Jacobs

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arXiv · 0911.3834

Duality for Convexity

Bart Jacobs

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Abstract

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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Bart Jacobs. 2009-11-19. Duality for Convexity. https://arxiv.org/abs/0911.3834

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