Symmetric Monoidal Structure with Local Character is a Property

Stefano Gogioso
(University of Oxford)
Dan Marsden
(University of Oxford)
Bob Coecke
(University of Oxford)

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.

In Peter Selinger and Giulio Chiribella: Proceedings of the 15th International Conference on Quantum Physics and Logic (QPL 2018), Halifax, Canada, 3-7th June 2018, Electronic Proceedings in Theoretical Computer Science 287, pp. 179–190.
Published: 31st January 2019.

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