Pith. sign in

REVIEW 4 cited by

Braided Picard groups and graded extensions of braided tensor categories

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2006.08022 v2 pith:LUNMKEI6 submitted 2020-06-14 math.QA math.CT

Alexei Davydov , Dmitri Nikshych This is my paper · ORCID
classification math.QAmath.CT
keywords braidedcategoriespicardcategoricalextensionsgroupsfinitefunctors
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard group of $\cal B$ (consisting of invertible central $\cal B$-module categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane cohomology. We describe in detail braided $2$-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Clifford and Weyl algebras in symmetric tensor categories

    math.RT 2026-07 accept novelty 8.0 of 10

    For a symplectic object V in a Frobenius exact symmetric tensor category with finite symmetric algebra, the Weyl algebra A(V) is Azumaya, and the resulting symplectic Witt group is described by Stiefel-Whitney classes...

  2. Compact Semisimple Tensor 2-Categories are Morita Connected

    math.QA 2024-12 conditional novelty 7.0 of 10

    Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.

  3. On \'Etale Algebras and Bosonic Fusion 2-Categories

    math.CT 2024-11 conditional novelty 7.0 of 10

    Connected and Lagrangian étale algebras in Z_1(2Vect^π_G) are classified by subgroups, braided fusion categories with group actions, and 4-group morphism data; this yields a parametrization of bosonic fusion 2-categories.

  4. Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant

    hep-th 2024-12 conditional novelty 5.0 of 10

    New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.

Pith tools