49 citations · 159 across the 23 of their papers we have counts for
34 papers
Braided Picard groups and graded extensions of braided tensor categories
Alexei Davydov, Dmitri Nikshych
We classify various types of graded extensions of a finite braided tensor category in terms of its -categorical Picard groups. In particular, we prove that braided exte…
Cosimplicial monoids and deformation theory of tensor categories
Michael Batanin, Alexei Davydov
We introduce a notion of -commutativity () for cosimplicial monoids in a symmetric monoidal category , where corresponds to just cosimplicial mo…
Deformation cohomology of Schur-Weyl categories. Free symmetric categories
Alexei Davydov, Mohamed Elbehiry
The deformation cohomology of a tensor category controls deformations of its monoidal structure. Here we describe the deformation cohomology of tensor categories generated by one o…
Hopf algebra actions in tensor categories
Marcel Bischoff, Alexei Davydov
We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action all…
Third Cohomology and Fusion Categories
Alexei Davydov, Darren Simmons
It was observed recently that for a fixed finite group , the set of all Drinfeld centres of twisted by 3-cocycles form a group, the so-called group of modular extensions (of…
Autoequivalences of tensor categories attached to quantum groups at roots of
Alexei Davydov, Pavel Etingof, Dmitri Nikshych
We compute the group of braided tensor autoequivalences and the Brauer-Picard group of the representation category of the small quantum group , where…