Warning: this post is the "numerical" analog of Are there workable algebraic geometry approaches for the pentagon equation? I've replaced "algebraic geometry" by "numerical" in its content, ...
A pentagon equation is a system of polynomial equations of degree $3$ with several variables and integer coefficients, given by a fusion ring. A fusion ring is given by a finite set of integer ...
Can you find two finite groups G and H such that their representation categories are Morita equivalent (which is to say that there's an invertible bimodule category over these two monoidal categories) ...