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Constructing symmetric monoidal bicategories

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arxiv 1004.0993 v1 pith:6VL3QMRH submitted 2010-04-07 math.CT

Michael A. Shulman This is my paper · ORCID
classification math.CT
keywords monoidalsymmetricbicategoriescategoriesconstructingdoublemethodapplicable
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We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely applicable, though not universally so.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Premonoidal and Kleisli double categories

    math.CT 2024-01 unverdicted novelty 7.0 of 10

    Introduces premonoidal double categories and funny monoidal structures, proving equivalences to monoidal double categories and 1-1 correspondences for horizontal strengths on double monads.

  2. Iterated traces in 2-categories and Lefschetz theorems

    math.AT 2019-08 conditional novelty 7.0 of 10

    Iterated traces in any 2-dualizable symmetric monoidal bicategory commute, recovering and extending a wide family of Lefschetz-type theorems.

  3. Projective and anomalous representations of categories and their linearizations

    math.CT 2025-06 conditional novelty 6.0 of 10

    Anomalous representations of a category with anomaly J are equivalent to Vect-linear functors on the extension C^J and to scalar representations of the Stolz-Teichner subcategory C^J_ST.

  4. Networks of hybrid open systems

    math.DS 2019-08 accept novelty 6.0 of 10

    Hybrid open systems, their networks, and maps between networks are defined categorically, and maps between networks are shown to induce maps between the interconnected hybrid systems.

  5. 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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