Relation between bicrossed products and crossed extensions of fusion categories

2025/07/11 by Müller, Monique, Pollastri, Héctor Martín Peña, Plavnik, Julia
#18M20 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2507.08562

Abstract

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 between a pointed fusion category vec_G and a fusion category C can be realized as a bicrossed product vec_G\bowtie C.

Citations

• On bicrossed product of fusion categories and exact factorizations
• Fusion Categories over Non-Algebraically Closed Fields
• Exact factorizations and extensions of finite tensor categories
• Exact factorizations and extensions of fusion categories
• Exact sequences of tensor categories with respect to a module category
• Crossed actions of matched pairs of groups on tensor categories
• Morita equivalence methods in classification of fusion categories
• Exact sequences of tensor categories
• Classical and quantum conformal field theory

Related

• On bicrossed product of fusion categories and exact factorizations
• Extension theory for braided-enriched fusion categories
• Exact factorizations and extensions of fusion categories
• The Condensed Fiber Product and Zesting
• Rank-finiteness for G-crossed braided fusion categories