Computing associators of endomorphism fusion categories

Many applications of fusion categories, particularly in physics, require the associators or F F -symbols to be known explicitly. Finding these matrices typically involves solving vast systems coupled polynomial equations large numbers variables. In this work, we present an algorithm that allows associator data for some category with unknown computed from a Morita equivalent data. Given module over latter, utilize representation theory tube category, built data, compute When input is unitary, discuss how ensure obtained also unitary. We provide several worked examples illustrate algorithm. addition, include Mathematica files showing can used Haagerup \mathcal{H}_1 display="inline">ℋ1 , whose was previously unknown.