Tannaka duality

Tannaka duality is a mathematical concept that shows how a structured system, called a category, can be completely reconstructed from the symmetries (or automorphisms) of the representations it admits. Think of it like understanding an organization fully by examining its relationships and transformations. Specifically, it establishes an equivalence between certain mathematical objects (like groups) and categories of their linear representations, revealing that knowing how the system acts on examples allows you to recover the system itself. This powerful idea links abstract symmetries with concrete representations, deepening our understanding of their fundamental connections.