, Volume 5, Issue 2, pp 153-181
Date: 25 Dec 2010

Categorifications from planar diagrammatics

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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 and 7, 2009.