Space in monoidal categories

Pau Enrique Moliner, Chris Heunen, Sean Tull

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The category of Hilbert modules may be interpreted as a naive quantum field theory over a base space. Open subsets of the base space are recovered as idempotent subunits, which form a meet-semilattice in any firm braided monoidal category. There is an operation of restriction to an idempotent subunit: it is a graded monad on the category, and has the universal property of algebraic localisation. Spacetime structure on the base space induces a closure operator on the idempotent subunits. Restriction is then interpreted as spacetime propagation. This lets us study relativistic quantum information theory using methods entirely internal to monoidal categories. As a proof of concept, we show that quantum teleportation is only successfully supported on the intersection of Alice and Bob's causal future.
Original languageEnglish
Title of host publicationThe 14th International Conference on Quantum Physics and Logic (QPL)
PublisherOpen Publishing Association
Number of pages12
Publication statusPublished - 7 Jul 2017
Event14th International Conference on Quantum Physics and Logic - Nijmegen, Netherlands
Duration: 3 Jul 20177 Jul 2017

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherOpen Publishing Association
ISSN (Electronic)2075-2180


Conference14th International Conference on Quantum Physics and Logic
Abbreviated titleQPL 2017
Internet address


  • math.CT
  • quant-ph

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