Seminar

I will explain a definition of (op)lax natural transformations for (∞,n)-categories using the model of (complete) n-fold Segal spaces. The main step in the construction is to define a family of strict n-categories (more precisely, computads), which should be thought of as what one would expect to be a Gray tensor product of the walking l-fold compositions of k-morphisms. I will explain some immediate consequences of our definitions and focus on (pictures of) low-dimensional cases. The motivation for this project was to define ``twisted field theories’’, related to relative field theories, as suggested in work by Stolz-Teichner and Freed-Teleman. If requested by the audience, I will explain briefly what I mean by this. This was joint work with Theo Johnson-Freyd.