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arXiv · 1805.12088

Symmetric Monoidal Structure with Local Character is a Property

Stefano Gogioso·Dan Marsden·Bob Coecke
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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.

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Stefano Gogioso, Dan Marsden, Bob Coecke. 2018-05-30. Symmetric Monoidal Structure with Local Character is a Property. https://doi.org/10.4204/eptcs.287.10

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