# Algebraically closed higher categories

### APA

Johnson-Freyd, T. (2021). Algebraically closed higher categories. Perimeter Institute. https://pirsa.org/21120010

### MLA

Johnson-Freyd, Theo. Algebraically closed higher categories. Perimeter Institute, Dec. 03, 2021, https://pirsa.org/21120010

### BibTex

@misc{ pirsa_21120010, doi = {10.48660/21120010}, url = {https://pirsa.org/21120010}, author = {Johnson-Freyd, Theo}, keywords = {Mathematical physics}, language = {en}, title = {Algebraically closed higher categories}, publisher = {Perimeter Institute}, year = {2021}, month = {dec}, note = {PIRSA:21120010 see, \url{https://pirsa.org}} }

Theo Johnson-Freyd Dalhousie University

## Abstract

I will report on my progress, joint with David Reutter, to construct and analyze the algebraic closure of nVec – in other words, the universal n-category of framed nD TQFTs. The invertibles are Pontryagin dual to the stable homotopy groups of spheres. The Galois group is almost, but not quite, the stable PL group. An invertible TQFT can be condensed from the vacuum if and only if it trivializes on (possibly-exceptional) spheres.