Fusion operators and cocycloids in monoidal categories

Ross Street

doi:10.1023/A:1008655911796

Fusion operators and cocycloids in monoidal categories

Ross Street

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

The Yang-Baxter equation has been studied extensively in the context of monoidal categories. The fusion equation, which appears to be the Yang-Baxter equation with a term missing, has been studied mainly in the context of Hubert spaces. This paper endeavours to place the fusion equation in an appropriate categorical setting. Tricocycloids are defined; they are new mathematical structures closely related to Hopf algebras.

Original language	English
Pages (from-to)	177-191
Number of pages	15
Journal	Applied Categorical Structures
Volume	6
Issue number	2
DOIs	https://doi.org/10.1023/A:1008655911796
Publication status	Published - Jun 1998

Keywords

3-cocycle
Bialgebra
Braiding
Fusion equation
Hopf algebra
Monoidal category
String diagram
Tannaka duality
Tensor category

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10.1023/A:1008655911796

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AB - The Yang-Baxter equation has been studied extensively in the context of monoidal categories. The fusion equation, which appears to be the Yang-Baxter equation with a term missing, has been studied mainly in the context of Hubert spaces. This paper endeavours to place the fusion equation in an appropriate categorical setting. Tricocycloids are defined; they are new mathematical structures closely related to Hopf algebras.

KW - 3-cocycle

KW - Bialgebra

KW - Braiding

KW - Fusion equation

KW - Hopf algebra

KW - Monoidal category

KW - String diagram

KW - Tannaka duality

KW - Tensor category

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JO - Applied Categorical Structures

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ER -

Fusion operators and cocycloids in monoidal categories

Abstract

Keywords

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