Journal
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
Volume 19, Issue 5, Pages 769-820Publisher
BELGIAN MATHEMATICAL SOC TRIOMPHE
DOI: 10.36045/bbms/1354031551
Keywords
monoidal category; enriched category; braiding; string diagram; duoidal category; Mackey functor; Green functor; manifold invariant; topological quantum field theory; Day convolution; Joyal species; finite general linear group; link invariant; cuspidal representation
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Funding
- Australian Research Council Discovery Grant [DP1094883]
- Ecole de Mathematique, Universite catholique de Louvain
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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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