Computing associators of endomorphism fusion categories

Understand

Many applications of fusion categories, particularly in physics, require the associators or $F$-symbols to be known explicitly.

• Finding these matrices typically involves solving vast systems of coupled polynomial equations in large numbers of variables.
• In this work, we present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data.
• Given a module category over the latter, we utilize the representation theory of a module tube category, built from the known data, to compute this unknown associator data.