, Volume 27, Issue 2, pp 177–212 | Cite as

Quantum Logic in Dagger Kernel Categories

  • Chris Heunen
  • Bart Jacobs
Open Access


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.


Quantum logic Dagger kernel category Orthomodular lattice Categorical logic 


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© The Author(s) 2010

Authors and Affiliations

  1. 1.Oxford University Computing LaboratoryOxfordUK
  2. 2.Institute for Computing and Information Sciences (iCIS)Radboud University NijmegenNijmegenThe Netherlands

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