3. Braidings

Property F conjecture
If a fusion category has property F, then can’t use braiding alone for a universal quantum computer.Problem 3.1.
[Rowell] Given a braided, weakly integral fusion category, is the image of the braid group finite?
Is braided and weakly integral fusion equivalent to finite image of the braid group? 
Problem 3.3.
[Hagge, Wang] For unitary theories, we can choose a gauge so the $F$ matrices formed by the $6j$ symbols are unitary, and the braiding matrices are diagonal with respect to a certain basis. Can this happen for some nonunitary fusion category?
Is the unitarity of the $F$ matrices equivalent to unitarity?
Cite this as: AimPL: Classifying fusion categories, available at http://aimpl.org/fusioncat.