Chris Heunen

A Topos for Algebraic Quantum Theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos

Intuitionistic quantum logic of an n-level system

{\mathcal{T}(A)}

Active lattices determine AW*-algebras

in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra

Categorical semantics for arrows

{\underline{A}}

Characterizations of Categories of Commutative C*-Subalgebras

. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum