Open Access
december 2012 Monoidal categories in, and linking, geometry and algebra
Ross Street
Bull. Belg. Math. Soc. Simon Stevin 19(5): 769-820 (december 2012). DOI: 10.36045/bbms/1354031551


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, machinery 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.


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Ross Street. "Monoidal categories in, and linking, geometry and algebra." Bull. Belg. Math. Soc. Simon Stevin 19 (5) 769 - 820, december 2012.


Published: december 2012
First available in Project Euclid: 27 November 2012

zbMATH: 1267.18006
MathSciNet: MR3009017
Digital Object Identifier: 10.36045/bbms/1354031551

Primary: 18D10 , 18D20 , 18D35 , 20C08 , 20C30 , 20C33 , 57M25 , 81T45

Keywords: braiding , cuspidal representation , Day convolution , duoidal category , enriched category , finite general linear group , Green functor , Joyal species , link invariant , Mackey functor , manifold invariant , monoidal category , string diagram , topological quantum field theory

Rights: Copyright © 2012 The Belgian Mathematical Society

Vol.19 • No. 5 • december 2012
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