164 citations · 201 across the 10 of their papers we have counts for
11 papers
Hopf polyads
Alain Bruguières
We introduce Hopf polyads in order to unify Hopf monads and group actions on monoidal categories. A polyad is a lax functor from a small category (its source) to the bicategory of…
On normal tensor functors and coset decompositions for fusion categories
S. Burciu, A. Bruguières
We introduce the notion of double cosets relative to two fusion subcategories of a fusion category. Given a tensor functor $F : \C \to \D$ between fusion categories, we introduce a…
The doubles of a braided Hopf algebra
Alain Bruguières, Alexis Virelizier
Let A be a Hopf algebra in a braided rigid category B. In the case B admits a coend C, which is a Hopf algebra in B, we defined in 2008 the double D(A) of A, which is a quasitriang…
On the center of fusion categories
Alain Bruguières, Alexis Virelizier
Müger proved in 2003 that the center of a spherical fusion category C of non-zero dimension over an algebraically closed field is a modular fusion category whose dimension is the s…
Central Exact Sequences of Tensor Categories, Equivariantization and Applications
Alain Bruguières, Sonia Natale
We define equivariantization of tensor categories under tensor group scheme actions and give necessary and sufficient conditions for an exact sequence of tensor categories to be an…
Exact sequences of tensor categories
Alain Bruguières, Sonia Natale
We introduce the notions of normal tensor functor and exact sequence of tensor categories. We show that exact sequences of tensor categories generalize strictly exact sequences of…