Simple 2-representations and Classification of Categorifications

By Troels Agerholm
PhD Dissertations
October 2011
Abstract:
We consider selfadjoint functors defined on categories of modules over finite dimensional algebras and classify those that satisfy some simple relations. In particular we classify self- adjoint idempotents and selfadjoint squareroots of a multiple of the identity functor. This is related to the theory of algebraic categorification which we review with the viewpoint that a genuine categorification is a 2-representation of a 2-category.
Thesis advisor: Henning Haahr Andersen
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