Monoidal categories in, and linking, geometry and algebra
Monoidal categories in, and linking, geometry and algebra
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DOI：
10.36045/bbms/1354031551
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发表时间：
2012-01
期刊：
影响因子：
--
通讯作者：
R. Street
中科院分区：
文献类型：
--
作者：
R. Street
这是一篇关于monoidal范畴的理论和应用的报告。第一节通过向量空间范畴的例子介绍主要概念。弦符号的解释和自然导致结理论和monoidal类别之间的联系。第二部分回顾了由monoidal范畴理论的机器，如辫子和卷积，对表示论的各个方面所带来的启示。第三部分回顾了Mackey函子的范畴理论。一些最近的材料和猜想monoidal中心。第四节也是最后一节探讨了monoidal范畴被用于低维流形的新不变量和理论物理学的场论的方法。
This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a link between knot theory and monoidal categories. The second section reviews the light thrown on aspects of representation theory by the machinery of monoidal category theory, such as braidings and convolution. The category theory of Mackey functors is reviewed in the third section. Some recent material and a conjecture concerning monoidal centres is included. The fourth and final section looks at ways in which monoidal categories are, and might, be used for new invariants of low-dimensional manifolds and for the field theory of theoretical physics.