  To the working physicist, anyon theory is meant to describe certain
quasi-particle excitations occurring in two dimensional topologically ordered
systems. A typical calculation using this theory will involve operations such
as $\otimes$ to combine anyons, $F^{abc}_{d}$ to re-associate such
combinations, and $R^{ab}_c$ to commute or braid these anyons. Although there
is a powerful string-diagram notation that greatly assists these manipulations,
we still appear to be operating on particles arranged on a one-dimensional
line, algebraically ordered from left to right. The obvious question is, where
is the other dimension? The topological framework for considering these anyons
as truly living in a two dimensional space is known as a modular functor, or
topological quantum field theory. In this work we show how the apparently
one-dimensional algebraic anyon theory is secretly the theory of anyons living
in a fully two-dimensional system. The mathematical literature covering this
secret is vast, and we try to distill this down into something more manageable.
