21-23 octobre 2015
Institut de Mathématiques de Toulouse
Fuseau horaire Europe/Paris
21-23 Octobre 2015, Institut de Mathématiques de Toulouse

(Op)lax natural transformations for higher categories, relative quantum field theories, and the "even higher" Morita category

23 oct. 2015 à 11:40
Amphi Schwartz, bat. 1R3 (Institut de Mathématiques de Toulouse)

Amphi Schwartz, bat. 1R3

Institut de Mathématiques de Toulouse

118 Route de Narbonne 31068 Toulouse
Exposé de recherche sur invitation TopAlg


Dr Claudia Scheimbauer (Max Planck Institute for Mathematics, Bonn)


A relative (also called twisted) quantum field theory should be some transformation between quantum field theories, which themselves are symmetric monoidal functors out of a space-time category. In examples, the notion of natural transformation turns out to be too strong, making it necessary to relax it. In joint work with Theo Johson-Freyd we provide a framework for both lax and oplax transformations and their higher analogs, known as transfors, between strong $(\infty, n)$-functors. It is given by a double $(\infty,n)$-category built out of the target $(\infty, n)$-category that we call its (op)lax square, which governs the desired diagrammatics. Lax or oplax transfors then are functors into parts of the oplax square. Finally, I will explain how to use the (op)lax square to extend the construction of the higher Morita category of $E_d$-algebras in an $(\infty,n)$-category $\mathcal C$ to an even higher level using the higher morphisms of $\mathcal C$.

Auteur principal

Dr Claudia Scheimbauer (Max Planck Institute for Mathematics, Bonn)


Dr Theo Johnson-Freyd (Northwestern)

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