The chromatic Brauer category and its linear representations
The Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Applied categorical structures
Year: 2021, Volume: 29, Issue: 2, Pages: 349-377 |
| ISSN: | 1572-9095 |
| DOI: | 10.1007/s10485-020-09619-5 |
| Online Access: | Resolving-System, kostenfrei, Volltext: https://doi.org/10.1007/s10485-020-09619-5 Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s10485-020-09619-5 
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| Author Notes: | L. Felipe Müller, Dominik J. Wrazidlo |
| Summary: | The Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in which the morphisms are component-wise labeled. Linear representations of the (chromatic) Brauer category are symmetric strict monoidal functors into the category of real vector spaces and linear maps equipped with the Schauenburg tensor product. We study representation theory of the (chromatic) Brauer category, and classify all its faithful linear representations. As an application, we use indices of fold lines to construct a refinement of Banagl’s concrete positive TFT based on fold maps into the plane. |
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| Item Description: | Published online: 2 December 2020 Gesehen am 23.06.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1572-9095 |
| DOI: | 10.1007/s10485-020-09619-5 |