TL;DR
This paper demonstrates the existence of infinitely many fusion categories with Grothendieck rings that cannot be categorified in a pseudounitary way, highlighting limitations in categorification.
Contribution
It proves the existence of infinitely many inequivalent fusion categories lacking pseudounitary categorifications, a novel insight into fusion category theory.
Findings
Infinitely many inequivalent fusion categories identified.
Grothendieck rings without pseudounitary categorifications.
Highlights limitations in categorification approaches.
Abstract
We prove there exist infinitely many inequivalent fusion categories whose Grothendieck rings do not admit any pseudounitary categorifications.
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