Convexity, Duality and Effects

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.

• Type: Journal
• Year: 2010
• Where: IFIPTCS
• Authors: Bart Jacobs
• Keywords: Convex Functors, Effect Algebras, IFIPTCS 2010, Probability Distribution Functors, Theoretical Computer Science