Categorifications of Dihedral Groups
Alstad, Colin Erik
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Categorification is a term that was coined by Louis Crane and Igor Frenkel to describe the process of refounding mathematical theories from their bases in set theory to category theoretical analogs. In this thesis we provide a brief review of the theory of complex linear representations of the dihedral groups, provide the needed category theory background to define and discuss abelian categories and related structures, present the basic notions of algebraic categorification especially as it relates to representation theory, and finally detail how we can construct, and fail to construct, certain categorifications of the simple representations of the dihedral group <em>D<sub>3</sub></em>.