Quantum Logic in Dagger Kernel Categories

Chris Heunen, Bart Jacobs

Research output: Contribution to journalArticlepeer-review

Abstract

This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categorical/logical/order-theoretic properties, in terms of kernel fibrations, such as existence of pullbacks, factorisation, orthomodularity, atomicity and completeness. For instance, the Sasaki hook and and-then connectives are obtained, as adjoints, via the existential-pullback adjunction between fibres.
Original languageEnglish
Pages (from-to)177-212
Number of pages36
JournalOrder
Volume27
Issue number2
DOIs
Publication statusPublished - 2010

Keywords

  • Quantum logic
  • Dagger kernel category
  • Orthomodular lattice
  • Categorical logic

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