Duality for Convexity
Logic
2009-11-20 v1 Category Theory
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.
Cite
@article{arxiv.0911.3834,
title = {Duality for Convexity},
author = {Bart Jacobs},
journal= {arXiv preprint arXiv:0911.3834},
year = {2009}
}