Categorifications from planar diagrammatics
Mikhail Khovanov

TL;DR
This paper discusses diagrammatic methods for categorification, focusing on functors, natural transformations, and biadjointness, and reviews graphical descriptions of Soergel bimodules and quantum groups, based on Takagi lectures.
Contribution
It provides a comprehensive overview of diagrammatic categorification techniques and their applications to quantum groups and Soergel bimodules.
Findings
Diagrammatic presentation of functors and transformations
Graphical description of Soergel bimodules
Categorification of quantum groups
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research
