# Colloque 2015 du GDR 2875, Topologie Algébrique et Applications

Oct 21 – 23, 2015
Institut de Mathématiques de Toulouse
Europe/Paris timezone
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

Oct 23, 2015, 11:40 AM
50m
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

### Speaker

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

### Description

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 $\mathcal C$.

### Primary author

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

### Co-author

Dr Theo Johnson-Freyd (Northwestern)

### Presentation materials

There are no materials yet.