Categorifications from planar diagrammatics
M. Khovanov
Abstract: A diagrammatic presentation of functors and natural transformations and the virtues of biadjointness are discussed. We then review a graphical description of the category of Soergel bimodules and a diagrammatic categorification of positive halves of quantum groups. These notes are a write-up of Takagi Lectures given by the author in Hokkaido University in June 2009.