Categorification of Dijkgraaf-Witten Theory
Amit Sharma, Alexander A. Voronov
TL;DR
This paper develops a categorification of Dijkgraaf-Witten theory using cohomology with coefficients in a Picard groupoid, aiming to establish a foundation for constructing it as an Extended Topological Quantum Field Theory.
Contribution
It introduces a novel approach to categorify Dijkgraaf-Witten theory through cohomology with Picard groupoid coefficients, providing a new theoretical framework.
Findings
Framework for categorification of Dijkgraaf-Witten theory
Use of Picard groupoid of hermitian lines in cohomology
Foundation for extended TQFT construction
Abstract
The goal of the paper is to categorify Dijkgraaf-Witten theory, aiming at providing foundation for a direct construction of Dijkgraaf-Witten theory as an Extended Topological Quantum Field Theory. The main tool is cohomology with coefficients in a Picard groupoid, namely the Picard groupoid of hermitian lines.
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