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Finite matrices are complete for (dagger-)hypergraph categories

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arxiv 1406.5942 v2 pith:JVZLWUZX submitted 2014-06-23 math.CT

Aleks Kissinger This is my paper · ORCID
classification math.CT
keywords categoriescompletefinitehypergraphmatricesdagger-hypergraphmonoidalalgebra
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Hypergraph categories are symmetric monoidal categories where each object is equipped with a special commutative Frobenius algebra (SCFA). Dagger-hypergraph categories are the same, but with dagger-symmetric monoidal categories and dagger-SCFAs. In this paper, we show that finite matrices over a field K of characteristic 0 are complete for hypergraph categories, and that finite matrices where K has a non-trivial involution are complete for dagger-hypergraph categories.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 12 citations worldwide. Full citation record

  1. A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

    math.ST 2019-08 conditional novelty 7.0 of 10

    Markov categories provide a synthetic, axiom-based framework in which conditional independence, sufficiency, completeness, and classical theorems such as Basu and Bahadur hold uniformly across many probability theories.

  2. Foundations of Digital Circuits: Denotation, Operational, and Algebraic Semantics

    cs.LO 2025-02 conditional novelty 6.0 of 10

    A sound and complete denotational, operational, and algebraic semantics for synchronous sequential circuits with arbitrary feedback, plus a hypergraph rewriting framework for digital circuits.

  3. Double Categories of Open Systems: the Cospan Approach

    math.CT 2025-09 conditional novelty 4.0 of 10

    Structured and decorated cospan double categories for open systems have an exoskeleton/outer shell structure, and every object in them is a special symmetric Frobenius pseudomonoid.

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