Diagrammatics for Coxeter groups and their braid groups
  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. 
Ben Elias and Geordie Williamson
math.RT math.GT