Japan. J. Math. 5, 153--181 (2010)

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.


* This article is based on the 6th Takagi Lectures that the author delivered at the Hokkaido University on June 6--7, 2009.