TL;DR
This paper explores how categorification naturally arises in various geometric contexts such as sheaves and quantizations, using index formulas to connect classical and categorical geometric representation theory.
Contribution
It provides a unified framework for understanding categorification across different geometric settings and demonstrates how index formulas facilitate categorical calculations.
Findings
Categorification appears naturally in coherent and constructible sheaves.
Index formulas enable straightforward categorical calculations.
Classical geometric representation theory is related to categorical approaches.
Abstract
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform categorical calculations, and readily relate classical constructions of geometric representation theory to categorical ones.
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Taxonomy
TopicsAdvanced Algebra and Logic · Constraint Satisfaction and Optimization