Until recently, a careful derivation of the fusion structure of anyons from some underlying physical principles has been lacking. In Shi et al. (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 Kitaev (2006) and assuming that there are finitely many distinct topological charges, we arrive at the framework of ribbon categories.

直到最近，还缺少从某些基本物理原理中仔细推导任意子的融合结构的方法。在Shi等人中。（2020年），作者通过从2D间隙系统的纠缠面积定律的猜想形式入手，实现了这一目标。在这项工作中，我们改从交换对称原理开始，并确定与单一带状融合类别接触所需的其他假定的最小处方，作为对任何正则进行建模的适当代数框架。假设二维拟粒子在空间上是局部的，我们建立一个从有色辫子群到一个有限维希尔伯特空间类别的函子。使用此函子，我们构建了一个精确的交换对称性概念，从而使我们能够恢复任意子的核心融合特性。特别是给定一个系统$ñ$ 准粒子，我们证明了一定的作用 $ñ$-编织 ${\beta }_{ñ}$唯一指定其超选扇区。然后，我们将概述在通常的编织条件下任何人的编织和融合结构$6Ĵ$融合系统。通过假定Kitaev（2006）的对偶公理，并假设有限地存在许多不同的拓扑电荷，我们得出了功能区类别的框架。