<p>In the representation theory of finite-dimensional algebras, Gabriel showed that everything boils down to quivers: every algebra is Morita equivalent to a quotient of the path algebra of a quiver. I will discuss the generalisation of this result in the setting of fusion categories, including the “classification of finite-representation type quivers” in this setting, which now involve *all* finite Coxeter groups. These are combinations of joint work with Ben Elias and Mateusz Stroiński.</p>
