12 papers · 1 filter
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…
On the representation type of a finite tensor category
Petter Andreas Bergh, Karin Erdmann, Julia Yael Plavnik +1
Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the categ…
Relation between bicrossed products and crossed extensions of fusion categories
Monique Müller, Héctor MartÃn Peña Pollastri, Julia Plavnik
We show that all crossed extensions defined by Natale can be recovered as duals of bicrossed products of fusion categories. As an application, we prove that any exact factorization…
On bicrossed product of fusion categories and exact factorizations
Monique Müller, Héctor MartÃn Peña Pollastri, Julia Plavnik
We introduce the notion of a matched pair of fusion rings and fusion categories, generalizing the one for groups. Using this concept, we define the bicrossed product of fusion ring…
Generalised Orbifolds and G-equivariantisation
Sebastian Heinrich, Julia Plavnik, Ingo Runkel +1
In a construction motivated by topological field theory, a so-called orbifold datum in a ribbon category allows one to define a new ribbon category $C_{\mathbb{A}}…
On the finite generation of the cohomology of bosonizations
Nicolás Andruskiewitsch, David Jaklitsch, Van C. Nguyen +4
We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable fi…