Revista de la
Unión Matemática Argentina
Relation between bicrossed products and crossed extensions of fusion categories
Monique Müller, Héctor Martín Peña Pollastri, and Julia Plavnik

Volume 69, no. 1 (2026), pp. 281–294    

Published online (final version): March 3, 2026

https://doi.org/10.33044/revuma.5338

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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 $\mathrm{vec}_G$ and a fusion category $\mathcal{C}$ can be realized as a bicrossed product between $\mathrm{vec}_G$ and $\mathcal{C}$.

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