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The 2-Deligne Tensor Product

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arxiv 2103.16880 v2 pith:U5QUQAR5 submitted 2021-03-31 math.QA

Thibault D. Décoppet This is my paper · ORCID
classification math.QA
keywords tensordeligneproductcategoriescompactsemisimpleprovecategory
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abstract

We prove that the 2-Deligne tensor product of two compact semisimple 2-categories exists. Further, under suitable hypotheses, we explain how to describe the $Hom$-categories, connected components, and simple objects of a 2-Deligne tensor product. Finally, we prove that the 2-Deligne tensor product of two compact semisimple tensor 2-categories is a compact semisimple tensor 2-category.

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Cited by 2 Pith papers

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

  1. Compact Semisimple Tensor 2-Categories are Morita Connected

    math.QA 2024-12 conditional novelty 7.0 of 10

    Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.

  2. Orthonormal bases for higher Hilbert spaces

    math.QA 2026-08 conditional novelty 6.0 of 10

    For finite-dimensional 3-Hilbert spaces, orthonormal bases exist uniquely up to contractible choice, and the Yoneda embedding into the presheaf 3-Hilbert space is an isometric equivalence.

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