Tetrahedral symmetry of 6j-symbols in fusion categories

Understand

We establish tetrahedral symmetries of 6j-symbols for arbitrary fusion categories under minimal assumptions.

• As a convenient tool for our calculations we introduce the notion of a veined fusion category, which is generated by a finite set of simple objects but is larger than its skeleton.
• Every fusion category C contains veined fusion subcategories that are monoidally equivalent to C and which suffice to compute many categorical properties for C.
• The notion of a veined fusion category does not assume the presence of a pivotal structure, and thus in particular does not assume unitarity.