A cogroupoid associated to preregular forms
Hongdi Huang, Van C. Nguyen, Charlotte Ure, Kent B. Vashaw, Padmini, Veerapen, Xingting Wang
TL;DR
This paper constructs a family of cogroupoids linked to preregular forms, connecting them to known algebraic equivalences and exploring their twists within pivotal tensor categories.
Contribution
It introduces a new family of cogroupoids associated with preregular forms and analyzes their 2-cocycle twists in pivotal tensor categories.
Findings
Revealed Morita-Takeuchi equivalence for certain algebras
Developed categorical framework for preregularity
Analyzed twists of cogroupoids in pivotal categories
Abstract
We construct a family of cogroupoids associated to preregular forms and recover the Morita-Takeuchi equivalence for Artin-Schelter regular algebras of dimension two, observed by Raedschelders and Van den Bergh. Moreover, we study the 2-cocycle twists of pivotal analogues of these cogroupoids, by developing a categorical description of preregularity in any tensor category that has a pivotal structure.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra