Abstract
In this chapter we take a short break from Soergel bimodules to learn about diagrammatics. We illustrate the method of string diagrams for drawing morphisms in 2-categories and contrast it with the way that they are typically drawn. By viewing a monoidal category as a 2-category with a single object, we are also able to draw morphisms in monoidal categories. With these diagrams in hand, we then define the Temperley–Lieb category. In subsequent chapters we will use string diagrams to understand the morphisms in the monoidal category of Soergel bimodules.
This chapter is based on expanded notes of a lecture given by the authors and taken by
Anna Cepek and Andrew Stephens
A. Cepek
Department of Mathematical Sciences, Montana State University, Bozeman, MT, USA
A. Stephens Department of Mathematics, University of Oregon, Eugene, OR, USA
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References
C. Kassel, Quantum Groups. Graduate Texts in Mathematics, vol. 155 (Springer, New York, 1995), pp. xii+531. https://doi.org/10.1007/978-1-4612-0783-2
A.D. Lauda, An introduction to diagrammatic algebra and categorified quantum \(\mathfrak {sl}_2\). Bull. Inst. Math. Acad. Sin. (N.S.) 7(2), 165–270 (2012)
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Elias, B., Makisumi, S., Thiel, U., Williamson, G. (2020). How to Draw Monoidal Categories. In: Introduction to Soergel Bimodules. RSME Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48826-0_7
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DOI: https://doi.org/10.1007/978-3-030-48826-0_7
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