The chromatic Brauer category and its linear representations

• Verfasst von: Müller, Luis Felipe [VerfasserIn]
• Verfasst von: Wrazidlo, Dominik [VerfasserIn]
• Titel: The chromatic Brauer category and its linear representations
• Verf.angabe: L. Felipe Müller, Dominik J. Wrazidlo
• Jahr: 2021
• Umfang: 29 S.
• Fussnoten: Published online: 2 December 2020 ; Gesehen am 23.06.2021
• Titel Quelle: Enthalten in: Applied categorical structures
• Ort Quelle: Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993
• Jahr Quelle: 2021
• Band/Heft Quelle: 29(2021), 2, Seite 349-377
• ISSN Quelle: 1572-9095
• DOI: doi:10.1007/s10485-020-09619-5
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1761089404
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.