Abstract : This paper describes some basic relationships between mathematical structures that are relevant in quantum logic and probability, namely convex sets, effect algebras, and a new class of functors that we call 'convex functors'; they include what are usually called probability distribution functors. These relationships take the form of three adjunctions. Two of these three are 'dual' adjunctions for convex sets, one time with the Boolean truth values {0,1} as dualising object, and one time with the probablity values [0,1]. The third adjunction is between effect algebras and convex functors.
https://hal.inria.fr/hal-01054454 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Wednesday, August 6, 2014 - 4:24:59 PM Last modification on : Wednesday, August 9, 2017 - 12:03:27 PM Long-term archiving on: : Wednesday, November 26, 2014 - 12:58:21 AM
Bart Jacobs. Convexity, Duality and Effects. 6th IFIP TC 1/WG 2.2 International Conference on Theoretical Computer Science (TCS) / Held as Part of World Computer Congress (WCC), Sep 2010, Brisbane, Australia. pp.1-19, ⟨10.1007/978-3-642-15240-5_1⟩. ⟨hal-01054454⟩