The Drinfeld centre of a symmetric fusion category is 2-fold monoidal

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The Drinfeld centre of a symmetric fusion category is 2-fold monoidal. / Wasserman, Thomas A.

In: Advances in Mathematics, Vol. 366, 107090, 2020.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Wasserman, TA 2020, 'The Drinfeld centre of a symmetric fusion category is 2-fold monoidal', Advances in Mathematics, vol. 366, 107090. https://doi.org/10.1016/j.aim.2020.107090

APA

Wasserman, T. A. (2020). The Drinfeld centre of a symmetric fusion category is 2-fold monoidal. Advances in Mathematics, 366, [107090]. https://doi.org/10.1016/j.aim.2020.107090

Vancouver

Wasserman TA. The Drinfeld centre of a symmetric fusion category is 2-fold monoidal. Advances in Mathematics. 2020;366. 107090. https://doi.org/10.1016/j.aim.2020.107090

Author

Wasserman, Thomas A. / The Drinfeld centre of a symmetric fusion category is 2-fold monoidal. In: Advances in Mathematics. 2020 ; Vol. 366.

Bibtex

@article{ef9ba5d9cf7d45999f785cae2ffe1f80,
title = "The Drinfeld centre of a symmetric fusion category is 2-fold monoidal",
abstract = "We show that the Drinfeld centre of a symmetric fusion category over an algebraically closed field of characteristic zero is a bilax 2-fold monoidal category. That is, it carries two monoidal structures, the convolution and symmetric tensor products, that are bilax monoidal functors with respect to each other. We additionally show that the braiding and symmetry for the convolution and symmetric tensor products are compatible with this bilax structure. We establish these properties without referring to Tannaka duality for the symmetric fusion category. This has the advantage that all constructions are done purely in terms of the fusion category structure, making the result easy to use in other contexts.",
keywords = "2-Fold monoidal, Category theory, Drinfeld centre, Fusion category",
author = "Wasserman, {Thomas A.}",
year = "2020",
doi = "10.1016/j.aim.2020.107090",
language = "English",
volume = "366",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - The Drinfeld centre of a symmetric fusion category is 2-fold monoidal

AU - Wasserman, Thomas A.

PY - 2020

Y1 - 2020

N2 - We show that the Drinfeld centre of a symmetric fusion category over an algebraically closed field of characteristic zero is a bilax 2-fold monoidal category. That is, it carries two monoidal structures, the convolution and symmetric tensor products, that are bilax monoidal functors with respect to each other. We additionally show that the braiding and symmetry for the convolution and symmetric tensor products are compatible with this bilax structure. We establish these properties without referring to Tannaka duality for the symmetric fusion category. This has the advantage that all constructions are done purely in terms of the fusion category structure, making the result easy to use in other contexts.

AB - We show that the Drinfeld centre of a symmetric fusion category over an algebraically closed field of characteristic zero is a bilax 2-fold monoidal category. That is, it carries two monoidal structures, the convolution and symmetric tensor products, that are bilax monoidal functors with respect to each other. We additionally show that the braiding and symmetry for the convolution and symmetric tensor products are compatible with this bilax structure. We establish these properties without referring to Tannaka duality for the symmetric fusion category. This has the advantage that all constructions are done purely in terms of the fusion category structure, making the result easy to use in other contexts.

KW - 2-Fold monoidal

KW - Category theory

KW - Drinfeld centre

KW - Fusion category

UR - http://www.scopus.com/inward/record.url?scp=85080134467&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2020.107090

DO - 10.1016/j.aim.2020.107090

M3 - Journal article

AN - SCOPUS:85080134467

VL - 366

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 107090

ER -

ID: 260679381