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arXiv · 2507.08562

Relation between bicrossed products and crossed extensions of fusion categories

Monique Müller·Héctor Martín Peña Pollastri·Julia Plavnik
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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 $\operatorname{vec}_G$ and a fusion category $\mathcal{C}$ can be realized as a bicrossed product $\operatorname{vec}_G\bowtie \mathcal{C}$.

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Monique Müller, Héctor Martín Peña Pollastri, Julia Plavnik. 2025-07-11. Relation between bicrossed products and crossed extensions of fusion categories. https://doi.org/10.33044/revuma.5338

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