Monoidal categories in, and linking, geometry and algebra

Ross Street*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)769-820
    Number of pages52
    JournalBulletin of the Belgian Mathematical Society - Simon Stevin
    Volume19
    Issue number5
    Publication statusPublished - 2012

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