A field guide to categories with $A_n$ fusion rules

Understand

We collate information about the fusion categories with $A_n$ fusion rules.

• This note includes the classification of these categories, a realisation via the Temperley-Lieb categories, the auto-equivalence groups (both braided and tensor), identifications of the subcategories of invertible objects, and explicit descriptions of the Drinfeld centres.
• The first section describes the classification of these categories (as monoidal, dagger, pivotal, and braided categories).
• The second section describes the properties of these categories.