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21-23 octobre 2015
Institut de Mathématiques de Toulouse
Europe/Paris timezone
21-23 Octobre 2015, Institut de Mathématiques de Toulouse
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Contribution Exposé de recherche sur invitation

Institut de Mathématiques de Toulouse - Amphi Schwartz, bat. 1R3

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


  • Dr. Claudia SCHEIMBAUER

Auteurs principaux


Abstract content

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 $\mathcal C$.