Axioms for the category of Hilbert spaces

Chris Heunen, Andre Kornell

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematical foundations of quantum theory raised in reconstruction programmes such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke.
Original languageEnglish
Article numbere2117024119
Number of pages5
JournalProceedings of the National Academy of Sciences (PNAS)
Issue number9
Early online date25 Feb 2022
Publication statusPublished - 25 Feb 2022

Keywords / Materials (for Non-textual outputs)

  • Hilbert space
  • monoidal category
  • colimit


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