  We introduce the notion of a $\textit{reflection fusion category}$, which is
a type of a $G$-crossed category generated by objects of Frobenius-Perron
dimension $1$ and $\sqrt{p}$, where $p$ is an odd prime. We show that such
categories correspond to orthogonal reflection groups over $\mathbb{F}_p$. This
allows us to use the known classification of irreducible reflection groups over
finite fields to classify irreducible reflection fusion categories.

Quantum Algebra