Tannaka-Krein duality is a powerful theoretical framework that establishes a correspondence between certain categories of algebraic objects and their associated representation categories. This duality highlights the relationship between a Hopf algebra and its category of representations, showing how one can recover the original algebraic structure from the representation theory. It connects the ideas of algebra, geometry, and topology, particularly in the context of both Hopf algebras and compact matrix quantum groups.
congrats on reading the definition of Tannaka-Krein duality. now let's actually learn it.