Frobenius reciprocity for multifiat 2-categories

Powell, Aberdeen (2024) Frobenius reciprocity for multifiat 2-categories. Doctoral thesis, University of East Anglia.

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Abstract

This thesis has a single goal, namely the establishment of a form of Frobenius reciprocity for finitary birepresentations of multifiat 2-categories.

Multifiat 2-categories are the 2-categorical analogues of finite dimensional associative algebras with involution. Our first novel result is an explicit form of correspondence between birepresentations, morphisms of birepresentations and modifications on the one hand, and coalgebras, bicomodules and morphisms of bicomodules on the other hand. In the latter context, there is a natural definition of induction of birepresentations along a pseudofunctor, while in the former, there is a natural notion of restriction, completely analogous to other representation theories. We use our correspondence to define both in the same setting, that of coalgebras and bicomodules.

We show that restriction and induction are adjoint as pseudofunctors, given some technical assumptions.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
Depositing User:	Kitty Laine
Date Deposited:	04 Nov 2025 14:49
Last Modified:	04 Nov 2025 14:49
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100900
DOI:

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