含缺陷的域论与中心函子
Field theories with defects and the centre functor
摘要：
本文介绍了含缺陷的量子场论的函子形式。在对一般维度的模型作了一些评论之后，我们将自己限制在两个维度上--最低维度，在这两个维度中存在着有缺陷的有趣的域论。我们研究了一些细节，这种模型的最简单的例子，即拓扑域论的缺陷，我们通过晶格TFT描述。最后，我们给出了一个应用在代数中，缺陷TFT为我们提供了一个函定义的中心的代数。这涉及将交换代数的目标类别改变为双类别。在本文中，我们强调的作用，高阶范畴-在我们的情况下双范畴-在描述域论的缺陷。
英文摘要：
This note is intended as an introduction to the functorial formulation of quantum field theories with defects. After some remarks about models in general dimension, we restrict ourselves to two dimensions - the lowest dimension in which interesting field theories with defects exist. We study in some detail the simplest example of such a model, namely a topological field theory with defects which we describe via lattice TFT. Finally, we give an application in algebra, where the defect TFT provides us with a functorial definition of the centre of an algebra. This involves changing the target category of commutative algebras into a bicategory. Throughout this paper, we emphasise the role of higher categories - in our case bicategories - in the description of field theories with defects.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
