  Until recently, a careful derivation of the fusion structure of anyons from
some underlying physical principles has been lacking. In [Shi et al., Ann.
Phys., 418 (2020)], the authors achieved this goal by starting from a
conjectured form of entanglement area law for 2D gapped systems. In this work,
we instead start with the principle of exchange symmetry, and determine the
minimal prescription of additional postulates needed to make contact with
unitary ribbon fusion categories as the appropriate algebraic framework for
modelling anyons. Assuming that 2D quasiparticles are spatially localised, we
build a functor from the coloured braid groupoid to the category of
finite-dimensional Hilbert spaces. Using this functor, we construct a precise
notion of exchange symmetry, allowing us to recover the core fusion properties
of anyons. In particular, given a system of $n$ quasiparticles, we show that
the action of a certain $n$-braid $\beta_{n}$ uniquely specifies its
superselection sectors. We then provide an overview of the braiding and fusion
structure of anyons in the usual setting of braided $6j$ fusion systems. By
positing the duality axiom of [A. Kitaev, Ann. Phys., 321(1) (2006)] and
assuming that there are finitely many distinct topological charges, we arrive
at the framework of ribbon categories.
