Q-system Completeness of Unitary Connections

TL;DR

This paper proves that every Q-system in a categorified setting of unitary connections splits, advancing the understanding of algebraic structures in C*-tensor categories.

Contribution

It establishes the splitting property of Q-systems within the categorified framework of unitary connections, extending prior algebraic results.

Findings

Every Q-system in UC splits

Categorification of Bratteli diagrams and unitary connections

Advancement in the structure theory of Q-systems

Abstract

A Q-system is a unitary version of a separable Frobenius algebra object in a C*-tensor category. In a recent joint work with P. Das, S. Ghosh and C. Jones, the author has categorified Bratteli diagrams and unitary connections by building a $2$-category \textbf{UC}. We prove that every $Q$-system in \textbf{UC} splits.