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Quantum Sets of Compact Quantum Groups

Mainak Ghosh

Abstract

Q-system completion can be thought of as a notion of higher idempotent completion of C*-2-categories. We introduce a notion of quantum bi-elements, and study Q-system completion in the context of compact quantum groups. We relate our notion of quantum bi-elements to already known notions of quantum sets and quantum functions, and provide a description of Q-system completion of the C*-2-category of compact quantum groups using quantum bi-elements

Quantum Sets of Compact Quantum Groups

Abstract

Q-system completion can be thought of as a notion of higher idempotent completion of C*-2-categories. We introduce a notion of quantum bi-elements, and study Q-system completion in the context of compact quantum groups. We relate our notion of quantum bi-elements to already known notions of quantum sets and quantum functions, and provide a description of Q-system completion of the C*-2-category of compact quantum groups using quantum bi-elements
Paper Structure (8 sections, 16 theorems, 40 equations)

This paper contains 8 sections, 16 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations related to 2-categories
  4. Q-system completion
  5. Compact quantum groups
  6. Graphical calculus in Hilbert spaces
  7. Bimodules of compact quantum groups
  8. Quantum bi-elements

Key Result

Theorem 1.1

$\mathcal{G}$ is a locally idempotent complete C*-2-category.

Theorems & Definitions (51)

  • Theorem 1.1
  • Proposition 1.2
  • Theorem 1.3
  • Definition 2.1
  • Remark 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • ...and 41 more