Hokkaido Mathematical Journal

Distributors on a tensor category

D. TAMBARA

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Abstract

Let $\cA$ be a tensor category and let $\cV$ denote the category of vector spaces. A distributor on $\cA$ is a functor $\cA^{\op}\times \cA\to \cV$. We are concerned with distributors with two-sided $\cA$-action. Those distributors form a tensor category, which we denoted by ${}_{\cA}\bD(\cA,\cA)_{\cA}$. The functor category $\Hom(\cA^{\op},\cV)$ is also a tensor category and has the center $\bZ(\Hom(\cA^{\op},\cV))$. We show that if $\cA$ is rigid, then ${}_{\cA}\bD(\cA,\cA)_{\cA}$ and $\bZ(\Hom(\cA^{\op},\cV))$ are equivalent as tensor categories.

Article information

Source
Hokkaido Math. J., Volume 35, Number 2 (2006), 379-425.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766362

Digital Object Identifier
doi:10.14492/hokmj/1285766362

Mathematical Reviews number (MathSciNet)
MR2254657

Zentralblatt MATH identifier
1103.18009

Subjects
Primary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]

Keywords
tensor category distributor center

Citation

TAMBARA, D. Distributors on a tensor category. Hokkaido Math. J. 35 (2006), no. 2, 379--425. doi:10.14492/hokmj/1285766362. https://projecteuclid.org/euclid.hokmj/1285766362


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