  This expository article supplies the mathematical background underpinning the
braid representation calculator introduced in arXiv:2212.00831; those
representations describe the sets of logic gates available to a topological
quantum computer for processing encoded qubits. Assuming little background in
category theory, we first recall the notion of a ribbon fusion category (RFC),
collecting most of the necessary definitions. Then we discuss how certain RFCs
arise from the representation theory of quantum groups. We explore the braiding
in these categories in detail, since it is essential for the quantum computing
application.
