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We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if the associated braid group representations factor over a finite group, and suggest that categories of integral Frobenius-Perron dimension are precisely those with property F.
We establish rank-finiteness for the class of $G$-crossed braided fusion categories, generalizing the recent result for modular categories and including the important case of braided fusion categories. This necessitates a study of slightly degenerate
For a braided fusion category $mathcal{V}$, a $mathcal{V}$-fusion category is a fusion category $mathcal{C}$ equipped with a braided monoidal functor $mathcal{F}:mathcal{V} to Z(mathcal{C})$. Given a fixed $mathcal{V}$-fusion category $(mathcal{C}, m
The Witt group of nondegenerate braided fusion categories $mathcal{W}$ contains a subgroup $mathcal{W}_text{un}$ consisting of Witt equivalence classes of pseudo-unitary nondegenerate braided fusion categories. For each finite-dimensional simple Lie
This is a study of weakly integral braided fusion categories with elementary fusion rules to determine which possess nondegenerately braided extensions of theoretically minimal dimension, or equivalently in this case, which satisfy the minimal modula
We show that braidings on a fusion category $mathcal{C}$ correspond to certain fusion subcategories of the center of $mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and group-theoretical fusion categories.