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We give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated planar graphs. This presentation extends the Coxeter presentation. We deduce a simple criterion for a Coxeter group or braid group to act on a category.
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Ben Elias, Geordie Williamson, Diagrammatics for Coxeter groups and their braid groups. Quantum Topol. 8 (2017), no. 3, pp. 413–457DOI 10.4171/QT/94