Category of SET Orders - Representation Principle for Symmetry Enriched Topological Orders

Explore the representation principle for studying physical systems with given symmetries in this comprehensive lecture on symmetry enriched topological (SET) orders. Delve into the appropriate representation category, known as the category of SET orders, and discover how it encodes crucial information about the interplay between symmetry and topological orders for fusion n-category symmetries. Examine various aspects of SET orders, including defects, boundaries, symmetry charges, symmetry breaking, stacking, gauging of generalized symmetry, and quantum currents. Learn about a detailed categorical algorithm for computing generalized gauging, and understand the proof that gauging is always reversible as a special type of Morita-equivalence. Gain insights into the explicit data for ungauging, which serves as the inverse to gauging, in this in-depth exploration of SET order categories.

Tian Lan: Category of SET orders #ICBS2024