6 papers
Putting the Brauer back in Brauer-Picard
Sean Sanford
We establish a 6-term left exact sequence, involving Galois cohomology of the base field , and the Brauer-Picard groupoid of a fusion category. This generalizes a result…
Pivotal Brauer-Picard groupoids and graded extensions
Agustina Czenky, David Jaklitsch, Dmitri Nikshych +4
We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard -categorical groups and realize them as fixed points…
Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
Diogo Andrade, Julia Bierent, Jennifer Brown +28
These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of…
Compact Semisimple Tensor 2-Categories are Morita Connected
Thibault D. Décoppet, Sean Sanford
In arXiv:2211.04917, it was shown that, over an algebraically closed field of characteristic zero, every fusion 2-category is Morita equivalent to a connected fusion 2-category, th…
Fusion Categories over Non-Algebraically Closed Fields
Sean Sanford
Several complications arise when attempting to work with fusion categories over arbitrary fields. Here we describe some of the new phenomena that occur when the field is not algebr…
Invertible Fusion Categories
Sean Sanford, Noah Snyder
A tensor category over a field is said to be invertible if there's a tensor category such that is Morita…