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Quantum Physics

arXiv:1805.12088v2 (quant-ph)
[Submitted on 30 May 2018 (v1), last revised 29 Jan 2019 (this version, v2)]

Title:Symmetric Monoidal Structure with Local Character is a Property

Authors:Stefano Gogioso (University of Oxford), Dan Marsden (University of Oxford), Bob Coecke (University of Oxford)
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Abstract:In previous work we proved that, for categories of free finite-dimensional modules over a commutative semiring, linear compact-closed symmetric monoidal structure is a property, rather than a structure. That is, if there is such a structure, then it is uniquely defined (up to monoidal equivalence). Here we provide a novel unifying category-theoretic notion of symmetric monoidal structure with local character, which we prove to be a property for a much broader spectrum of categorical examples, including the infinite-dimensional case of relations over a quantale and the non-free case of finitely generated modules over a principal ideal domain.
Comments: In Proceedings QPL 2018, arXiv:1901.09476
Subjects: Quantum Physics (quant-ph); Category Theory (math.CT)
Cite as: arXiv:1805.12088 [quant-ph]
  (or arXiv:1805.12088v2 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1805.12088
Journal reference: EPTCS 287, 2019, pp. 179-190
Related DOI: https://doi.org/10.4204/EPTCS.287.10

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Wed, 30 May 2018 17:07:01 UTC (594 KB)
[v2] Tue, 29 Jan 2019 05:38:11 UTC (37 KB)
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