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We collate information about the fusion categories with $A_n$ fusion rules.This note includes the classification of these categories, a realisation viathe Temperley-Lieb categories, the auto-equivalence groups (both braided andtensor), identifications of the subcategories of invertible objects, andexplicit descriptions of the Drinfeld centres. The first section describes theclassification of these categories (as monoidal, dagger, pivotal, and braidedcategories). The second section describes the properties of these categories.

A field guide to categories with $A_n$ fusion rules