论文标题
对拓扑命令和类别理论的邀请
An invitation to topological orders and category theory
论文作者
论文摘要
尽管这是一个众所周知的事实，但二十年来，拓扑秩序的研究需要这种类别理论，但对于学生和工作物理学家来说，掌握类别理论的抽象语言仍然是一个非平凡的挑战。在这项工作中，对于那些没有类别理论背景的人来说，我们很好地详细说明了（编织）融合类别的结构如何自然地来自晶格模型和物理直觉。此外，我们表明，融合类别中的几乎所有数学概念和构造及其表示理论，例如（单型）函子，德林菲尔德中心，模块类别，莫里塔等效性，凝结完成和融合2类，自然来自晶格模型和物理直觉。在此过程中，我们还介绍了一些拓扑顺序的基本概念和重要结果。
Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for students and working physicists to master the abstract language of category theory. In this work, for those who have no background in category theory, we explain in great details how the structure of a (braided) fusion category naturally emerges from lattice models and physical intuitions. Moreover, we show that nearly all mathematical notions and constructions in fusion categories and its representation theory, such as (monoidal) functors, Drinfeld center, module categories, Morita equivalence, condensation completion and fusion 2-categories, naturally emerge from lattice models and physical intuitions. In this process, we also introduce some basic notions and important results of topological orders.
