Generalisations and specifications in the categorification of representation theory

Macpherson, James (2020) Generalisations and specifications in the categorification of representation theory. Doctoral thesis, University of East Anglia.

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Abstract

We extend the 2-representation theory of finitary 2-categories in two separate fashions. For the first, we examine certain 2-categories with infinitely many objects, called locally finitary 2-categories, and for the second we examine certain 2-categories with infinitely many isomorphism classes of indecomposable 1-morphisms, called (locally) wide finitary 2-categories. In both cases, we extend various classification results relating to transitive and simple transitive 2-representations to the new setting, and provide examples where this new theory applies. Most prominently, we generalise the classification of simple transitive cell 2-representations of fiat 2-categories by cell 2-representations to the locally finitary setting (and further extend it to the weakly fiat case), and we generalise to both settings the classification of all transitive 2-representations of weakly fiat 2-categories as equivalent to 2-representations associated to coalgebra 1-morphisms.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Chris White
Date Deposited: 21 Jul 2021 10:52
Last Modified: 21 Jul 2021 10:52
URI: https://ueaeprints.uea.ac.uk/id/eprint/80674
DOI:

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