Title: Diagrams for Gray categories With Duals
Speaker: Catherine Meusburger, FAU Erlangen-Nürnberg
Date: Tuesday, September 24, 2013
Time: 2:00pm – 3:30pm
Place: Seminar Room 313, Simons Center
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Abstract: Tricategories play an important role as the algebraic data that characterises defects in 3d TFTs. In oriented TFTs, an appropriate notion of duals in the tricategory is needed to implement orientation reversal. We define such duals for Gray categories, which can be viewed as maximally strict tricategories, and analyse their algebraic properties. This is done via a diagrammatic calculus, which generalises the diagrammatic calculus for ribbon categories and relates the duals in the Gray category to the geometry of the defects. This is joint work with Gregor Schaumann and John Barrett.